Per Håkan Lundow
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Per Håkan Lundow has a total of 12 co-authors. Here are the top co-authors by number of shared publications:
- Klas Markström
Umeå Universitet Umeå Sweden
7 shared publications A. Rosengren
Condensed Matter Theory, Department of Theoretical Physics , AlbaNova University Center , KTH, SE-106 91, Stockholm, Sweden
3 shared publications- Anders Rosengren
Condensed Matter Theory Department of Theoretical Physics AlbaNova University Center KTH SE-106 91 Stockholm Sweden
3 shared publications - Alexander V. Balatsky
Theoretical Division Los Alamos National Laboratory 87545 Los Alamos NM
2 shared publications - Anders Rosengren
Department of Physics, AlbaNova University Center, KTH, SE-106 91 Stockholm, Sweden
2 shared publications - Daniel Andrén
Department of Mathematics, Umeå University, SE-901 87 Umeå, Sweden
2 shared publications
Latest Publications
- 2 January 2013
- Published by Taylor & Francis in Philosophical Magazine
- Vol. 93 (14) , 1755-1770
Thep,q-binomial distribution applied to the 5d Ising model
The leading order form of the magnetization distribution is well-known for the 5d Ising model close to . Its corrections-to-scaling are not known though. Since we have earlier established that this distribution is extremely well-fitted by a -binomial distribution, we report considerably longer series expansions for its moments in terms of three parameters, providing new details on the scaling behaviour of the Ising distribution and its moments near . As applications, we give for example the scaling formulas for the ratios , and the full distribution at .
- 2 January 2013
- Published by Taylor & Francis in Philosophical Magazine
- Vol. 93 (14) , 1755-1770
Thep,q-binomial distribution applied to the 5d Ising model
The leading order form of the magnetization distribution is well-known for the 5d Ising model close to . Its corrections-to-scaling are not known though. Since we have earlier established that this distribution is extremely well-fitted by a -binomial distribution, we report considerably longer series expansions for its moments in terms of three parameters, providing new details on the scaling behaviour of the Ising distribution and its moments near . As applications, we give for example the scaling formulas for the ratios , and the full distribution at .
- Open Access
Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative -dS/dU. In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi first order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered. Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed.
Open AccessNon-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative -dS/dU. In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi first order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered. Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed.
- 5 July 2010
- Published by Taylor & Francis in Philosophical Magazine
- Vol. 90 (24) , 3313-3353
On thep,q-binomial distribution and the Ising model
We employ p, q-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case p = q. We apply our investigation to the simple d-dimensional lattices for d = 1, 2, 3, 4, 5 and fit p, q-binomial distributions to our data, some of which are exact but most are sampled. For d = 1 and d = 5, the magnetisation distributions are remarkably well-fitted by p,q-binomial distributions. For d = 4 we are only slightly less successful, while for d = 2, 3 we see some deviations (with exceptions!) between the p, q-binomial and the Ising distribution. However, at certain temperatures near T c the statistical moments of the fitted distribution agree with the moments of the sampled data within the precision of sampling. We begin the paper by giving results of the behaviour of the p, q-distribution and its moment growth exponents given a certain parameterisation of p, q. Since the moment exponents are known for the Ising model (or at least approximately for d = 3) we can predict how p, q should behave and compare this to our measured p, q. The results speak in favour of the p, q-binomial distribution's correctness regarding its general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution, however, is not settled.
- 5 July 2010
- Published by Taylor & Francis in Philosophical Magazine
- Vol. 90 (24) , 3313-3353
On thep,q-binomial distribution and the Ising model
We employ p, q-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case p = q. We apply our investigation to the simple d-dimensional lattices for d = 1, 2, 3, 4, 5 and fit p, q-binomial distributions to our data, some of which are exact but most are sampled. For d = 1 and d = 5, the magnetisation distributions are remarkably well-fitted by p,q-binomial distributions. For d = 4 we are only slightly less successful, while for d = 2, 3 we see some deviations (with exceptions!) between the p, q-binomial and the Ising distribution. However, at certain temperatures near T c the statistical moments of the fitted distribution agree with the moments of the sampled data within the precision of sampling. We begin the paper by giving results of the behaviour of the p, q-distribution and its moment growth exponents given a certain parameterisation of p, q. Since the moment exponents are known for the Ising model (or at least approximately for d = 3) we can predict how p, q should behave and compare this to our measured p, q. The results speak in favour of the p, q-binomial distribution's correctness regarding its general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution, however, is not settled.
- Open Access
On the $p,q$-binomial distribution and the Ising model
A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ $p,q$-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case $p=q$. We take our investigation to the simple $d$-dimensional lattices for $d=1,2,3,4,5$ and fit $p,q$-binomial distributions to our data, some of which are exact but most are sampled. For $d=1$ and $d=5$ the magnetisation distributions are remarkably well-fitted by $p,q$-binomial distributions. For $d=4$ we are only slightly less successful, while for $d=2,3$ we see some deviations (with exceptions!) between the $p,q$-binomial and the Ising distribution. We begin the paper by giving results on the behaviour of the $p,q$-distribution and its moment growth exponents given a certain parameterization of $p,q$. Since the moment exponents are known for the Ising model (or at least approximately for $d=3$) we can predict how $p,q$ should behave and compare this to our measured $p,q$. The results speak in favour of the $p,q$-binomial distribution's correctness regarding their general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution is not settled though.Open AccessOn the $p,q$-binomial distribution and the Ising model
A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ $p,q$-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case $p=q$. We take our investigation to the simple $d$-dimensional lattices for $d=1,2,3,4,5$ and fit $p,q$-binomial distributions to our data, some of which are exact but most are sampled. For $d=1$ and $d=5$ the magnetisation distributions are remarkably well-fitted by $p,q$-binomial distributions. For $d=4$ we are only slightly less successful, while for $d=2,3$ we see some deviations (with exceptions!) between the $p,q$-binomial and the Ising distribution. We begin the paper by giving results on the behaviour of the $p,q$-distribution and its moment growth exponents given a certain parameterization of $p,q$. Since the moment exponents are known for the Ising model (or at least approximately for $d=3$) we can predict how $p,q$ should behave and compare this to our measured $p,q$. The results speak in favour of the $p,q$-binomial distribution's correctness regarding their general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution is not settled though. - 3 September 2009
- Published by American Physical Society (APS) in Physical Review E
- Vol. 80 (3) , 031104
Critical behavior of the Ising model on the four-dimensional cubic lattice
In this paper we investigate the nature of the singularity of the Ising model of the four-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent but a nonrigorous field-theory argument predicts an unbounded specific heat with a logarithmic singularity at . We find that within the given accuracy the canonical ensemble data are consistent both with a logarithmic singularity and a bounded specific heat but that the microcanonical ensemble lends stronger support to a bounded specific heat. Our conclusion is that either much larger system sizes are needed for Monte Carlo studies of this model in four dimensions or the field-theory prediction of a logarithmic singularity is wrong.- 3 September 2009
- Published by American Physical Society (APS) in Physical Review E
- Vol. 80 (3) , 031104
Critical behavior of the Ising model on the four-dimensional cubic lattice
In this paper we investigate the nature of the singularity of the Ising model of the four-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent but a nonrigorous field-theory argument predicts an unbounded specific heat with a logarithmic singularity at . We find that within the given accuracy the canonical ensemble data are consistent both with a logarithmic singularity and a bounded specific heat but that the microcanonical ensemble lends stronger support to a bounded specific heat. Our conclusion is that either much larger system sizes are needed for Monte Carlo studies of this model in four dimensions or the field-theory prediction of a logarithmic singularity is wrong.- 1 August 2009
- Published by Taylor & Francis in Philosophical Magazine
- Vol. 89 (22-24) , 2009-2042
The Ising model for the bcc, fcc and diamond lattices: A comparison
A large-scale Monte Carlo simulation study of the Ising model for the simple cubic lattice was recently performed by us. In this paper, we complement that study with the bcc, fcc and diamond lattices. Both the canonical and microcanonical ensembles are employed. We give estimates of the critical temperature and also other quantities in the critical region. An analysis of the critical behaviour points to distinct high- and low-temperature exponents, especially for the specific heat, as was also obtained for the simple cubic lattice, although the agreement is good between the different lattices. The source of this discrepancy is briefly discussed.
- 1 August 2009
- Published by Taylor & Francis in Philosophical Magazine
- Vol. 89 (22-24) , 2009-2042
The Ising model for the bcc, fcc and diamond lattices: A comparison
A large-scale Monte Carlo simulation study of the Ising model for the simple cubic lattice was recently performed by us. In this paper, we complement that study with the bcc, fcc and diamond lattices. Both the canonical and microcanonical ensembles are employed. We give estimates of the critical temperature and also other quantities in the critical region. An analysis of the critical behaviour points to distinct high- and low-temperature exponents, especially for the specific heat, as was also obtained for the simple cubic lattice, although the agreement is good between the different lattices. The source of this discrepancy is briefly discussed.
- Open Access
The 1-vertex transfer matrix and accurate estimation of channel capacity
The notion of a 1-vertex transfer matrix for multi-dimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix. The method is applied to estimate the first 15 digits of the entropy of the 2-dimensional (0,1) run length limited channel. In order to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with a large scale computation of eigenvalues for the (0,1) run length limited channel in 2 and 3 dimensions have been carried out. This in turn leads to improvements on the best previous lower and upper bounds for that channel.
Open AccessThe 1-vertex transfer matrix and accurate estimation of channel capacity
The notion of a 1-vertex transfer matrix for multi-dimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix. The method is applied to estimate the first 15 digits of the entropy of the 2-dimensional (0,1) run length limited channel. In order to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with a large scale computation of eigenvalues for the (0,1) run length limited channel in 2 and 3 dimensions have been carried out. This in turn leads to improvements on the best previous lower and upper bounds for that channel.
- 9 April 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (13) , 134508
Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates
Inelastic neutron scattering data for YBaCuO as well as for LaSrCuO indicate incommensurate neutron scattering peaks with an incommensuration away from the point. can be replotted as a linear function of the incommensuration for these materials. This linear relation implies that the constant that relates these two quantities, where one is the incommensuration (momentum) and the other is (energy), has the dimension of velocity, which we denote by : . We argue that this experimentally determined relation can be obtained in a simple model of Josephson coupled stripes. Within this framework, we address the role of the isotope effect on . We assume that the incommensuration is set by the doping of the sample and is not sensitive to the oxygen isotope given the fixed doping. We find therefore that the only parameter that can change with the O isotope substitution in the relation is the velocity . We predict an oxygen isotope effect on and expect it to be .- 9 April 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (13) , 134508
Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates
Inelastic neutron scattering data for YBaCuO as well as for LaSrCuO indicate incommensurate neutron scattering peaks with an incommensuration away from the point. can be replotted as a linear function of the incommensuration for these materials. This linear relation implies that the constant that relates these two quantities, where one is the incommensuration (momentum) and the other is (energy), has the dimension of velocity, which we denote by : . We argue that this experimentally determined relation can be obtained in a simple model of Josephson coupled stripes. Within this framework, we address the role of the isotope effect on . We assume that the incommensuration is set by the doping of the sample and is not sensitive to the oxygen isotope given the fixed doping. We find therefore that the only parameter that can change with the O isotope substitution in the relation is the velocity . We predict an oxygen isotope effect on and expect it to be .- 8 February 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (7) , 073103
One-dimensional Kondo lattice model studied through numerical diagonalization
The one-dimensional Kondo lattice model is studied by means of the numerical diagonalization method. By using massively parallel computations, we were able to study lattices large enough to obtain convergent results for electron densities . For such densities, an additional ferromagnetic region is found inside the paramagnetic phase. Also, a region is found where the localized spins participate in the low-energy dynamics together with the conduction electrons, thus resulting in a large Fermi surface. These results are an independent confirmation of previous density matrix renormalization group results.- 8 February 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (7) , 073103
One-dimensional Kondo lattice model studied through numerical diagonalization
The one-dimensional Kondo lattice model is studied by means of the numerical diagonalization method. By using massively parallel computations, we were able to study lattices large enough to obtain convergent results for electron densities . For such densities, an additional ferromagnetic region is found inside the paramagnetic phase. Also, a region is found where the localized spins participate in the low-energy dynamics together with the conduction electrons, thus resulting in a large Fermi surface. These results are an independent confirmation of previous density matrix renormalization group results.- 1 January 2008
- Published by Wiley in LMS Journal of Computation and Mathematics
- Vol. 11, 1-14
Exact and Approximate Compression of Transfer Matrices for Graph Homomorphisms
The aim of this paper is to extend the previous work on transfer matrix compression in the case of graph homomorphisms. For H-homomorphisms of lattice-like graphs we demonstrate how the automorphisms of H, as well as those of the underlying lattice, can be used to reduce the size of the relevant transfer matrices. As applications of this method we give currently best known bounds for the number of 4- and 5-colourings of the square grid, and the number of 3- and 4-colourings of the three-dimensional cubic lattice. Finally, we also discuss approximate compression of transfer matrices.
- 1 January 2008
- Published by Wiley in LMS Journal of Computation and Mathematics
- Vol. 11, 1-14
Exact and Approximate Compression of Transfer Matrices for Graph Homomorphisms
The aim of this paper is to extend the previous work on transfer matrix compression in the case of graph homomorphisms. For H-homomorphisms of lattice-like graphs we demonstrate how the automorphisms of H, as well as those of the underlying lattice, can be used to reduce the size of the relevant transfer matrices. As applications of this method we give currently best known bounds for the number of 4- and 5-colourings of the square grid, and the number of 3- and 4-colourings of the three-dimensional cubic lattice. Finally, we also discuss approximate compression of transfer matrices.