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

International Journal of Modern Physics C

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

Synge Todo

Published Jun 1, 1999• 19 citations
Publisher

Abstract

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

DOI
10.1142/s0129183199000401

Related papers

Transfer-Matrix Study of Hard-Core Singularity for Hard-Square Lattice Gas

Synge Todo

A singularity on the negative fugacity axis of the hard-square lattice gas is investigated in terms of numerical diagonalization of transfer matrices. The location of the singular point $z_c^-$ and the critical exponent $ν$ are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge $c$ and the dominant scaling dimension $x_σ$ are -4.399996(8) and -0.3999996(7), respectively. These results strongly support that this singularity belongs to the same universality class as the Yang-Lee edge singularity ($c=-22/5, x_σ=-2/5 and ν=5/12$).

arXiv:cond-mat/9703176•Mar 19, 1997•3 citations

TRANSFER-MATRIX METHOD FOR HARD-SQUARE LATTICE GAS

Synge Todo, Masuo Suzuki

An improved sparse-matrix factorization technique for the transfer matrix of the hard-square lattice gas is proposed to perform exact diagonalization up to the strip width N = 34. The critical point, critical free-energy density, and universal parameters are determined accurately. The eigenvalue spectrum of the transfer matrix is also precisely investigated at the critical point for different boundary conditions.

International Journal of Modern Physics C•Dec 1, 1996•11 citations

Comment on ‘Series expansions from the corner transfer matrix renormalization group method: the hard-squares model’

Iwan Jensen

Earlier this year Chan extended the low-density series for the hard-squares partition function $κ(z)$ to 92 terms. Here we analyse this extended series focusing on the behaviour at the dominant singularity $z_d$ which lies on on the negative fugacity axis. We find that the series has a confluent singularity of order 2 at $z_d$ with exponents $θ=0.83333(2)$ and $θ'= 1.6676(3)$. We thus confirm that the exponent $θ$ has the exact value $\frac56$ as observed by Dhar.

arXiv:1208.1060•Journal of Physics A Mathematical and Theoretical•Nov 28, 2012•9 citations

Finite-size analysis of the hard-square lattice gas

Wenan Guo, Henk W. J. Blöte

We investigate the hard-square lattice-gas model by means of transfer-matrix calculations and a finite-size-scaling analysis. Using a minimal set of assumptions we find that the spectrum of correction-to-scaling exponents is consistent with that of the exactly solved Ising model, and that the critical exponents and correlation-length amplitudes closely follow the relation predicted by conformal invariance. Assuming that these spectra are exactly identical, and conformal invariance, we determine the critical point, the conformal anomaly, and the temperature and magnetic exponents with numerical margins of 10(-11) or less. These results are in a perfect agreement with the exactly known Ising universal parameters in two dimensions. In order to obtain this degree of precision, we included system sizes as large as feasible, and used extended-precision floating-point arithmetic. The latter resource provided a substantial improvement of the analysis, despite the fact that it restricted the transfer-matrix calculations to finite sizes of at most 34 lattice units.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Oct 30, 2002•52 citations

Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly

Tiago J. Oliveira, Jürgen F. Stilck

Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.

arXiv:1504.07956•Physical Review E•Sep 1, 2015•12 citations

The non-interacting hard-square lattice gas: Ising universality

G. Kamieniarz, Henk W. J. Blöte

The critical exponents of the non-interacting hard-square lattice gas model are determined by means of series analysis and finite-size scaling. The series analysis leads to results for the exponents that are consistent with the expected Ising universal values. A scaling analysis is performed on different types of numerical finite-size data obtained by means of the transfer-matrix method. The results support Ising universality. A procedure based on conformal invariance reproduces the known Ising temperature and magnetic exponents within 10 -6 . Furthermore we estimate the critical density of the hard-square model as rho c =0.367 743 000 (5).

Journal of Physics A Mathematical and General•Dec 7, 1993•33 citations
A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.
A singularity on the negative fugacity axis of the hard-square lattice gas is investigated in terms of numerical diagonalization of transfer matrices. The location of the singular point zc−z_c^-zc−​ and the critical exponent ννν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge ccc and the dominant scaling dimension xσx_σxσ​ are -4.399996(8) and -0.3999996(7), respectively. These results strongly support that this singularity belongs to the same universality class as the Yang-Lee edge singularity (c=−22/5,xσ=−2/5andν=5/12c=-22/5, x_σ=-2/5 and ν=5/12c=−22/5,xσ​=−2/5andν=5/12).
Earlier this year Chan extended the low-density series for the hard-squares partition function κ(z)κ(z)κ(z) to 92 terms. Here we analyse this extended series focusing on the behaviour at the dominant singularity zdz_dzd​ which lies on on the negative fugacity axis. We find that the series has a confluent singularity of order 2 at zdz_dzd​ with exponents θ=0.83333(2)θ=0.83333(2)θ=0.83333(2) and θ′=1.6676(3)θ'= 1.6676(3)θ′=1.6676(3). We thus confirm that the exponent θθθ has the exact value 56\frac5665​ as observed by Dhar.
We investigate the hard-square lattice-gas model by means of transfer-matrix calculations and a finite-size-scaling analysis. Using a minimal set of assumptions we find that the spectrum of correction-to-scaling exponents is consistent with that of the exactly solved Ising model, and that the critical exponents and correlation-length amplitudes closely follow the relation predicted by conformal invariance. Assuming that these spectra are exactly identical, and conformal invariance, we determine the critical point, the conformal anomaly, and the temperature and magnetic exponents with numerical margins of 10(-11) or less. These results are in a perfect agreement with the exactly known Ising universal parameters in two dimensions. In order to obtain this degree of precision, we included system sizes as large as feasible, and used extended-precision floating-point arithmetic. The latter resource provided a substantial improvement of the analysis, despite the fact that it restricted the transfer-matrix calculations to finite sizes of at most 34 lattice units.
Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.
The critical exponents of the non-interacting hard-square lattice gas model are determined by means of series analysis and finite-size scaling. The series analysis leads to results for the exponents that are consistent with the expected Ising universal values. A scaling analysis is performed on different types of numerical finite-size data obtained by means of the transfer-matrix method. The results support Ising universality. A procedure based on conformal invariance reproduces the known Ising temperature and magnetic exponents within 10 -6 . Furthermore we estimate the critical density of the hard-square model as rho c =0.367 743 000 (5).