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)

Infinite Range Ising Models with a Tricritical Point

B. S. Lee

Published Jan 1, 1982• 1 citation
Publisher

Abstract

Abstract Two infinite range Ising models are solved exactly using a microcanonical ensemble in the longrange order parameter. Classical tricritical points exist for both models. The first model involving two‐spin and four‐spin terms is relevant to the compressible Ising model. The other model is the infinite range version of the Blume‐Capel spin‐one Ising model. In both the cases the exact free‐energy functions calculated are examples of exact classical Landau free‐energy functions with tricritical point behaviour.

DOI
10.1002/pssb.2221090147

Related papers

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions*

Liangsheng Li

Abstract We explore the tricritical points and the critical lines of both Blume–Emery–Grifnths and Ising model within long-range interactions in the microcanonical ensemble. For K = K MTP , the tricritical exponents take the values β = 1/4, 1 = γ − ≠ γ + = 1/2 and 0 = α − ≠ α + = −1/2, which disagree with classical (mean held) values. When K > K MTP , the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K CTP ), where the values of the critical expoents become β = 1/2, 1 = γ − ≠ γ + = 2 and 0 = α − ≠ α + = 1.

Communications in Theoretical Physics•Dec 1, 2016•0 citations

Ensemble-dependent effect of disorder on multicritical points in a system with long-range interactions

Nir Schreiber, Reuven Cohen

We introduce two variants of the Blume--Emery--Griffiths model with long-range, mean-field-like interactions and quenched disorder. Although the two variants are described by different Hamiltonians, they yield the same free energy. Moreover, both Hamiltonians lead to the same average energy and hence to the same microcanonical entropy. The canonical and microcanonical phase boundaries differ markedly, and so does the multicritical behaviour of the two ensembles. In the microcanonical ensemble, tricritical points appear for any fraction of active spins, whereas in the canonical ensemble they emerge only when this fraction is sufficiently large. At lower fractions, canonical critical endpoints arise instead. We also report the formation of gaps in the entropy as a function of magnetization, another manifestation of ensemble inequivalence.

arXiv:2610.39929•Oct 29, 2026•0 citations

Tricriticality and the Blume-Capel model: A Monte Carlo study within the microcanonical ensemble

Markus Deserno

The microcanonical partition function ${\ensuremath{\Omega}}_{\ensuremath{\alpha},N}(E)$ of a three-dimensional ferromagnetic simple cubic Blume-Capel model is calculated for several coupling ratios $\ensuremath{\alpha}$ close to and on the first-order side of the tricritical point. To this end a single Monte Carlo simulation of a suitably extended partition function for systems of $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ spins with $L\ensuremath{\in}{8,10,12,14,18}$ was performed. A finite system analog of the latent heat is introduced in order to define a tricritical point in finite systems as well. An empirical scaling of its coordinates to the thermodynamic limit yields ${\ensuremath{\alpha}}^{(t)}=2.84479\ifmmode\pm\else\textpm\fi{}0.00030$ for the tricritical coupling ratio, and ${k}_{B}{T}^{(t)}/J=1.4182\ifmmode\pm\else\textpm\fi{}0.0055$ for the tricritical transition temperature. The results are compared with values obtained on fcc lattices.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 1997•75 citations

Tricritical Behavior of Ising Spin Glasses with Charge Fluctuations

Bernd Rosenow, R. Oppermann

We show that tricritical points displaying unusual behavior exist in phase diagrams of fermionic Ising spin glasses as the chemical potential or the filling assumes characteristic values. Exact results for infinite range interaction and a one-loop renormalization group analysis of thermal tricritical fluctuations for finite range models are presented. Surprising similarities with zero temperature transitions and a new $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ tricritical point of metallic quantum spin glasses are derived.

arXiv:cond-mat/9604015•Physical Review Letters•Aug 19, 1996•14 citations

Tricritical Universality in Two Dimensions

David Paul Landau, Robert H. Swendsen

A powerful, new extension of the Monte Carlo renormalization-group (MCRG) method is used to accurately determine the tricritical point and exponents in two very different two-dimensional models: an Ising antiferromagnet and a Blume-Capel model. We find four relevant tricritical eigenvalues which are essentially identical for both models. We also demonstrate that subtle warning signals appear in a standard Monte Carlo calculation when a second-order transition is being misinterpreted as first order.

Physical Review Letters•Jun 1, 1981•137 citations

Thermodynamic quantities and phase diagrams of spin-1 Blume–Capel bilayer Ising model

Ersin Kantar, Mehmet Ertaş

An effective field theory with correlations has been used to study the critical behavior of the spin-1 Blume–Capel bilayer Ising model on a square lattice. The effects of the Hamiltonian parameters on thermodynamic quantities and phase diagrams are investigated in detail. We found that the system exhibits the first and the second order transitions as well as tricritical point. Furthermore, we have observed that the change of tricritical point values depends on interaction parameters.

International Journal of Modern Physics B•Jun 23, 2015•9 citations
Abstract Two infinite range Ising models are solved exactly using a microcanonical ensemble in the longrange order parameter. Classical tricritical points exist for both models. The first model involving two‐spin and four‐spin terms is relevant to the compressible Ising model. The other model is the infinite range version of the Blume‐Capel spin‐one Ising model. In both the cases the exact free‐energy functions calculated are examples of exact classical Landau free‐energy functions with tricritical point behaviour.
Abstract We explore the tricritical points and the critical lines of both Blume–Emery–Grifnths and Ising model within long-range interactions in the microcanonical ensemble. For K = K MTP , the tricritical exponents take the values β = 1/4, 1 = γ − ≠ γ + = 1/2 and 0 = α − ≠ α + = −1/2, which disagree with classical (mean held) values. When K > K MTP , the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K CTP ), where the values of the critical expoents become β = 1/2, 1 = γ − ≠ γ + = 2 and 0 = α − ≠ α + = 1.
We introduce two variants of the Blume--Emery--Griffiths model with long-range, mean-field-like interactions and quenched disorder. Although the two variants are described by different Hamiltonians, they yield the same free energy. Moreover, both Hamiltonians lead to the same average energy and hence to the same microcanonical entropy. The canonical and microcanonical phase boundaries differ markedly, and so does the multicritical behaviour of the two ensembles. In the microcanonical ensemble, tricritical points appear for any fraction of active spins, whereas in the canonical ensemble they emerge only when this fraction is sufficiently large. At lower fractions, canonical critical endpoints arise instead. We also report the formation of gaps in the entropy as a function of magnetization, another manifestation of ensemble inequivalence.
The microcanonical partition function ${\ensuremath{\Omega}}_{\ensuremath{\alpha},N}(E)$ of a three-dimensional ferromagnetic simple cubic Blume-Capel model is calculated for several coupling ratios $\ensuremath{\alpha}$ close to and on the first-order side of the tricritical point. To this end a single Monte Carlo simulation of a suitably extended partition function for systems of $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ spins with $L\ensuremath{\in}{8,10,12,14,18}$ was performed. A finite system analog of the latent heat is introduced in order to define a tricritical point in finite systems as well. An empirical scaling of its coordinates to the thermodynamic limit yields ${\ensuremath{\alpha}}^{(t)}=2.84479\ifmmode\pm\else\textpm\fi{}0.00030$ for the tricritical coupling ratio, and ${k}_{B}{T}^{(t)}/J=1.4182\ifmmode\pm\else\textpm\fi{}0.0055$ for the tricritical transition temperature. The results are compared with values obtained on fcc lattices.
We show that tricritical points displaying unusual behavior exist in phase diagrams of fermionic Ising spin glasses as the chemical potential or the filling assumes characteristic values. Exact results for infinite range interaction and a one-loop renormalization group analysis of thermal tricritical fluctuations for finite range models are presented. Surprising similarities with zero temperature transitions and a new T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 tricritical point of metallic quantum spin glasses are derived.
A powerful, new extension of the Monte Carlo renormalization-group (MCRG) method is used to accurately determine the tricritical point and exponents in two very different two-dimensional models: an Ising antiferromagnet and a Blume-Capel model. We find four relevant tricritical eigenvalues which are essentially identical for both models. We also demonstrate that subtle warning signals appear in a standard Monte Carlo calculation when a second-order transition is being misinterpreted as first order.