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

physica status solidi (b)

A New Numerical Method for the Investigation of Finite Models in Statistical Mechanics

V. I. Dimitrov, K. I. Grozdev

Published Jan 1, 1995• 1 citation
Publisher
DOI
10.1002/pssb.2221870126

Related papers

Solving Models in Statistical Mechanics

R. J. Baxter

Elsevier eBooks•Jan 1, 1989•26 citations

Conformal invariance and critical exponents of the Takhtajan-Babujian models

Francisco Castilho Alcaraz, Marcio Jose Martins

The authors are concerned with the critical properties of antiferromagnetic Takhtajan-Babujian models with spin S=1, 3/2 and 2. The leading eigenenergies of this Hamiltonian, in a finite chain, are calculated by investigating numerically and analytically the Bethe ansatz equations for the finite system. The critical exponents and the conformal anomaly are obtained from their relations with the eigenspectrum of the finite Hamiltonian. The appearance of logarithmic corrections produces poor estimates. However, a combination of analytical and numerical methods produces very good estimates. Their results strongly support the conjecture that the Wess-Zumino-Witten-Novikov non-linear sigma models with topological charge k=2S are the underlying field theories for these spin-S statistical mechanics models.

Journal of Physics A Mathematical and General•Dec 7, 1988•45 citations

From Solitons to Knots and Links

Miki Wadati, Yasuhiro Akutsu

Development in the theory of solvable (integrable) models is reviewed. It covers from basic knowledge on completely integrable systems to recent work by the authors. First, soliton theory is briefly summarized. Through the inverse scattering method and its quantum extension, a central concept, commuting transfer matrices, and a key relation, the Yang-Baxter relation, are introduced. Second, it is shown that there exists at least ∞ × ∞ number of solvable models in two-dimensional statistical mechanics. Third, quantum spin chains corresponding to solvable statistical mechanical models are discussed. In particular, finite temperature extension of Baxter's formula is given. Fourth, a new approach is presented to the classification problem of knots and links. It is shown that link polynomial, topological invariant for knots and links, can be associated with any solvable model in statistical mechanics. In the presentation, universality of the soliton picture in field theory, spin systems and statistical mechanics is observed.

Progress of Theoretical Physics Supplement•Jan 1, 1988•46 citations

Methods in Statistical Mechanics

Osvaldo Civitarese, Manuel Gadella

Lecture notes in physics•Jan 1, 2020•6 citations

Methods in Statistical Mechanics: A Modern View

Osvaldo Civitarese, Manuel Gadella

•Sep 8, 2020•0 citations

On the Finite-Size Behavior of one Basic Model of Statistical Mechanics Describing Second Order Phase Transition

Daniel Dantchev

ABSTRACT: We present a short review and some new results on the finite-size behavior of finite systems exhibiting second order phase transition. We will be mainly focused on one basic model of statistical mechanics – the GinzburgLandau φ 4 model under the influence of temperature bath and an external ordering field.

Journal of Theoretical and Applied Mechanics/Mechanika Teoretyczna i Stosowana•Jan 1, 2021•1 citation
The authors are concerned with the critical properties of antiferromagnetic Takhtajan-Babujian models with spin S=1, 3/2 and 2. The leading eigenenergies of this Hamiltonian, in a finite chain, are calculated by investigating numerically and analytically the Bethe ansatz equations for the finite system. The critical exponents and the conformal anomaly are obtained from their relations with the eigenspectrum of the finite Hamiltonian. The appearance of logarithmic corrections produces poor estimates. However, a combination of analytical and numerical methods produces very good estimates. Their results strongly support the conjecture that the Wess-Zumino-Witten-Novikov non-linear sigma models with topological charge k=2S are the underlying field theories for these spin-S statistical mechanics models.
Development in the theory of solvable (integrable) models is reviewed. It covers from basic knowledge on completely integrable systems to recent work by the authors. First, soliton theory is briefly summarized. Through the inverse scattering method and its quantum extension, a central concept, commuting transfer matrices, and a key relation, the Yang-Baxter relation, are introduced. Second, it is shown that there exists at least ∞ × ∞ number of solvable models in two-dimensional statistical mechanics. Third, quantum spin chains corresponding to solvable statistical mechanical models are discussed. In particular, finite temperature extension of Baxter's formula is given. Fourth, a new approach is presented to the classification problem of knots and links. It is shown that link polynomial, topological invariant for knots and links, can be associated with any solvable model in statistical mechanics. In the presentation, universality of the soliton picture in field theory, spin systems and statistical mechanics is observed.