Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nuclear Physics B - Proceedings Supplements

Complex-temperature singularities of the susceptibility in the d = 2 Ising model

Robert E. Shrock

Published Apr 1, 1995• 6 citations
Publisher
DOI
10.1016/0920-5632(95)00379-n

Related papers

Complex-temperature singularities of Ising models

Robert E. Shrock

arXiv:hep-lat/9509054•Nuclear Physics B - Proceedings Supplements•Mar 1, 1996•0 citations

Logarithmic singularities of Q-dependent susceptibility of 2-D Ising model

Xiang‐Peng Kong, Helen Au-Yang, Jacques H. H. Perk

Physics Letters A•Nov 1, 1986•17 citations

Complex-temperature Ising model: Symmetry properties and behavior of correlation length and susceptibility

Giuseppe Marchesini, Robert E. Shrock

Nuclear Physics B•May 1, 1989•31 citations

Complex-temperature singularities of the susceptibility in the D=2 Ising model. I. Square lattice

V Matveev, Robert E. Shrock

We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that, as one approaches the point u=u s =-1 (where u=e '4K ) from within the complex extensions of the FM or AFM phases, the susceptibility has a divergent singularity of the form X approximately A s '(1+u)(- gamma s ') with exponent gamma s '=3/2. The critical amplitude A s ' is calculated. Other critical exponents are found to be alpha s '= sigma s =0 and beta s = 1/4 , so that the scaling relation alpha s '+2 beta s + gamma s ' is satisfied. However, using exact results for beta s on the square, triangular, and honeycomb lattices, we show that universality is violated at this singularity: beta s is lattice-dependent. Finally, from an analysis of spin-spin correlation functions, we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point u=-1 from within the symmetric phase. This is confirmed by an explicit study of high-temperature series expansions.

arXiv:hep-lat/9408020•Journal of Physics A Mathematical and General•Mar 23, 1995•63 citations

Complex-temperature properties of the 2D Ising model with beta H=+or-i pi /2

V. Matveev, Robert E. Shrock

We study the complex-temperature properties of a rare example of a statistical mechanical model which is exactly solvable in an external symmetry-breaking field, namely, the Ising model on the square lattice with beta H=+or-i pi /2. This model was solved by Lee and Yang (1952). We first determine the complex-temperature phases and their boundaries. From a low-temperature, high-field series expansion of the partition function, we extract the low-temperature series for the susceptibility chi to O(u 23 ), where u=e -4K . Analysing this series, we conclude that chi has divergent singularities (i) at u=u 3 =-(3-2 3 2/) with exponent gamma e '=5/4, (ii) at u=1, with exponent gamma 1 '=5/2, and (iii) at u=u s =-1, with exponent gamma s '=1. We also extract a shorter series for the staggered susceptibility and investigate its singularities. Using the exact result of Lee and Yang for the free energy, we calculate the specific heat and determine its complex-temperature singularities. We also carry this out for the uniform and staggered magnetization.

arXiv:hep-lat/9412105•Journal of Physics A Mathematical and General•Sep 7, 1995•39 citations

New results for the susceptibility of the two-dimensional Ising model at criticality

Xiang‐Peng Kong, Helen Au-Yang, Jacques H. H. Perk

Physics Letters A•May 1, 1986•23 citations
We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that, as one approaches the point u=u s =-1 (where u=e '4K ) from within the complex extensions of the FM or AFM phases, the susceptibility has a divergent singularity of the form X approximately A s '(1+u)(- gamma s ') with exponent gamma s '=3/2. The critical amplitude A s ' is calculated. Other critical exponents are found to be alpha s '= sigma s =0 and beta s = 1/4 , so that the scaling relation alpha s '+2 beta s + gamma s ' is satisfied. However, using exact results for beta s on the square, triangular, and honeycomb lattices, we show that universality is violated at this singularity: beta s is lattice-dependent. Finally, from an analysis of spin-spin correlation functions, we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point u=-1 from within the symmetric phase. This is confirmed by an explicit study of high-temperature series expansions.
We study the complex-temperature properties of a rare example of a statistical mechanical model which is exactly solvable in an external symmetry-breaking field, namely, the Ising model on the square lattice with beta H=+or-i pi /2. This model was solved by Lee and Yang (1952). We first determine the complex-temperature phases and their boundaries. From a low-temperature, high-field series expansion of the partition function, we extract the low-temperature series for the susceptibility chi to O(u 23 ), where u=e -4K . Analysing this series, we conclude that chi has divergent singularities (i) at u=u 3 =-(3-2 3 2/) with exponent gamma e '=5/4, (ii) at u=1, with exponent gamma 1 '=5/2, and (iii) at u=u s =-1, with exponent gamma s '=1. We also extract a shorter series for the staggered susceptibility and investigate its singularities. Using the exact result of Lee and Yang for the free energy, we calculate the specific heat and determine its complex-temperature singularities. We also carry this out for the uniform and staggered magnetization.