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

Physical review. B, Condensed matter

First-order phase transitions of Ising models with multispin interactions

Ole G. Mouritsen, Svend J. Knak Jensen, B. Frank

Published Feb 1, 1981• 20 citations
Publisher

Abstract

Ising models on fcc lattices with pure three-spin or pure four-spin interactions are shown by Monte Carlo calculations to exhibit only one phase transition which is of first order. The transition temperature of the model with pure four-spin interactions differs from the Onsager result. This implies that the model is likely not to possess a self-dual property as claimed by Wood.

DOI
10.1103/physrevb.23.976

Related papers

Two-dimensional Ising model with multispin interactions

Jean‐Marc Debierre, Loïc Turban

The two-dimensional Ising model in the rectangular lattice is generalised to include m-spin interactions in one direction and two-spin interactions in the other. This model is self-dual and the critical line is the same as in the conventional Ising model with m=2. The m=3 model is solved in a generalised mean-field approximation where the transition is first order. Using a phenomenological renormalisation group approach, approximate values of the thermal and magnetic exponents y t and y h are obtained for m=3 and m=4. The m=3 results together with symmetry arguments suggest that this model belongs to the same class of universality as the Baxter-Wu and four-state ferromagnetic Potts models. When m=4 the transition is probably first order.

Journal of Physics A Mathematical and General•Oct 21, 1983•39 citations

Universality and tricritical behavior of three-dimensional Ising models with two- and four-spin interactions

Ole G. Mouritsen, Svend J. Knak Jensen, B. Frank

The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-\textonehalf{} Ising model on an fcc lattice with mixtures of two- (${J}_{2}$) and four - (${J}_{4}$) spin interactions. In the limit ${J}_{2}=0$ the model exhibits a first-order transition. The transition remains of first order for $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\gtrsim}\frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\approx}\frac{1}{4}\ensuremath{-}\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{{J}_{4}}{{J}_{2}}\ensuremath{\lesssim}\frac{1}{4}$, the critical exponent $\ensuremath{\beta}$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.

Physical review. B, Condensed matter•Jul 1, 1981•27 citations

Phase transitions in systems with multispin interactions

K. A. Penson, Rémi Jullien, Pierre M. Pfeuty

An Ising-type model including $n$-spin nearest-neighbor interactions is introduced. The ground-state properties of its Hamiltonian version are studied in one and two dimensions. The model is self-dual in one dimension. The mean-field theory indicates that for $n>{n}_{c}$ the transition may become first order. Finite-size scaling suggests that ${n}_{c}=4$ in one dimension. The critical exponents as functions of $n$ are estimated.

Physical review. B, Condensed matter•Dec 1, 1982•78 citations

Monte Carlo simulation of type-1 fcc Ising antiferromagnets

Alto Stemmer, Alfred Hüller

Using Monte Carlo methods we investigate the phase transition of an Ising system on the fcc lattice, with antiferromagnetic nearest-neighbor interaction $J$ and ferromagnetic next-nearest-neighbor interaction $\ensuremath{\alpha}J$ for \ensuremath{\alpha} values up to 2. The scaling of the microcanonical entropy ${s}_{L}$ with system size $L$ agrees with the assumption of a first-order transition. Since the asymptotic behavior has not yet been reached, even for the largest systems with $L=40,$ our calculations cannot determine the order of the transition unambiguously.

Physical review. B, Condensed matter•Jul 1, 1998•8 citations

First- and second-order phase transitions in Heisenberg’s quantum model with multispin exchange

Akai Kurbanovich Murtazaev, I. A. Favorskii

First- and second-order phase transitions in the isotropic Heisenberg model with multispin exchange were investigated with the help of the quantum Monte Carlo method. The calculations were performed for a system with spin S = 1/2 and N = L3 spins (L = 8, 12, and 16) on simple cubic lattices with periodic boundary conditions. A relation between the pair and multispin exchange constants for which the second- order phase transitions are replaced by first-order phase transitions is established. First-order phase transitions have not been studied previously by the quantum Monte Carlo method. Phase diagrams were constructed for the model under study. The computational results are compared with the method of Green’s functions and the molecular-field theory.

Soviet Journal of Low Temperature Physics•Feb 1, 1992•0 citations

Monte Carlo Simulation of First Order Phase Transitions

Chunlei Wang, J. C. Li, M. L. Zhao +3 more

Monte Carlo simulation with Metropolis algorithm has been performed on a cubic Ising lattice with four-spin couplings. Temperature dependence of the spin average and average energy has been obtained. We found that the phase transition is of first order when the strength of four-spin coupling is stronger a critical value, and this critical value is of lattice size dependence. Binder cumulants still can be used to determine the second order phase transition temperature. For first order phase transition, the spin average disappears abruptly at the temperature of the average energy being a third of the ground state energy.

Ferroelectrics•Oct 29, 2010•10 citations
Ising models on fcc lattices with pure three-spin or pure four-spin interactions are shown by Monte Carlo calculations to exhibit only one phase transition which is of first order. The transition temperature of the model with pure four-spin interactions differs from the Onsager result. This implies that the model is likely not to possess a self-dual property as claimed by Wood.
The two-dimensional Ising model in the rectangular lattice is generalised to include m-spin interactions in one direction and two-spin interactions in the other. This model is self-dual and the critical line is the same as in the conventional Ising model with m=2. The m=3 model is solved in a generalised mean-field approximation where the transition is first order. Using a phenomenological renormalisation group approach, approximate values of the thermal and magnetic exponents y t and y h are obtained for m=3 and m=4. The m=3 results together with symmetry arguments suggest that this model belongs to the same class of universality as the Baxter-Wu and four-state ferromagnetic Potts models. When m=4 the transition is probably first order.
The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-\textonehalf{} Ising model on an fcc lattice with mixtures of two- (J2{J}_{2}J2​) and four - (J4{J}_{4}J4​) spin interactions. In the limit J2=0{J}_{2}=0J2​=0 the model exhibits a first-order transition. The transition remains of first order for $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\gtrsim}\frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\approx}\frac{1}{4}\ensuremath{-}\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{{J}_{4}}{{J}_{2}}\ensuremath{\lesssim}\frac{1}{4}$, the critical exponent $\ensuremath{\beta}$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.
An Ising-type model including nnn-spin nearest-neighbor interactions is introduced. The ground-state properties of its Hamiltonian version are studied in one and two dimensions. The model is self-dual in one dimension. The mean-field theory indicates that for n>ncn>{n}_{c}n>nc​ the transition may become first order. Finite-size scaling suggests that nc=4{n}_{c}=4nc​=4 in one dimension. The critical exponents as functions of nnn are estimated.
Using Monte Carlo methods we investigate the phase transition of an Ising system on the fcc lattice, with antiferromagnetic nearest-neighbor interaction JJJ and ferromagnetic next-nearest-neighbor interaction $\ensuremath{\alpha}J$ for \ensuremath{\alpha} values up to 2. The scaling of the microcanonical entropy sL{s}_{L}sL​ with system size LLL agrees with the assumption of a first-order transition. Since the asymptotic behavior has not yet been reached, even for the largest systems with L=40,L=40,L=40, our calculations cannot determine the order of the transition unambiguously.
First- and second-order phase transitions in the isotropic Heisenberg model with multispin exchange were investigated with the help of the quantum Monte Carlo method. The calculations were performed for a system with spin S = 1/2 and N = L3 spins (L = 8, 12, and 16) on simple cubic lattices with periodic boundary conditions. A relation between the pair and multispin exchange constants for which the second- order phase transitions are replaced by first-order phase transitions is established. First-order phase transitions have not been studied previously by the quantum Monte Carlo method. Phase diagrams were constructed for the model under study. The computational results are compared with the method of Green’s functions and the molecular-field theory.
Monte Carlo simulation with Metropolis algorithm has been performed on a cubic Ising lattice with four-spin couplings. Temperature dependence of the spin average and average energy has been obtained. We found that the phase transition is of first order when the strength of four-spin coupling is stronger a critical value, and this critical value is of lattice size dependence. Binder cumulants still can be used to determine the second order phase transition temperature. For first order phase transition, the spin average disappears abruptly at the temperature of the average energy being a third of the ground state energy.