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

Semina Ciências Exatas e Tecnológicas

Magnetoelasticidade e comportamento crítlco em cadeias de ising

André Tsutomu Ota, Silvio R. A. Salinas

Published Dec 15, 1989• 0 citations
Publisher

Abstract

We consider two distinct ways of introducing elastic degrees of freedom in the one-dimensional Ising model. Taking into account the average effect of elastic vibrations, the effective spin Hamiltonian in the pressure ensemble diplays long-rang interactions which give rise to a first-order phase transition. However, local fluctuation of the crystalline positions lead to an effective spin Hamiltonian with short-range interactions and without any thermodynamic anomaly in one dimension.

DOI
10.5433/1679-0375.1989v10n4p262

Related papers

Mixed-Order Phase Transition in a One-Dimensional Model

Amir Bar, David Mukamel

We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions that exhibits a mixed-order transition, namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models that are seemingly unrelated. The model we present serves as a link between two classes of models that exhibit a mixed-order transition in one dimension, namely, spin models with a coupling constant that decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.

arXiv:1309.4228•Physical Review Letters•Jan 7, 2014•81 citations

Crossover between short- and long-range interactions in the one-dimensional Ising model

V.B. Kislinsky, Vyacheslav I. Yukalov

The authors consider the one-dimensional Ising model which besides the interaction of nearest neighbours includes a long-range term. The latter is ferromagnetic while the nearest-neighbour interaction can have any sign. The crossover between short- and long-range interactions when varying the Hamiltonian parameters is analysed for such a model. For some values of the antiferromagnetic short-range interaction the transition from a ferro- to paramagnetic state is of first order. At the tricritical point where the transition order changes from second to first they obtain classical tricritical exponents. For a ferromagnetic short-range interaction the Curie temperature surpasses the transition temperature of the long-range model.

Journal of Physics A Mathematical and General•Jan 7, 1988•8 citations

Phase transitions in the one-dimensional Ising model with ferromagnetic and antiferromagnetic interactions

Dong Huang, Barbara J. Gabryś

A special case of the one-dimensional Ising model with short-range antiferromagnetic and long-range ferromagnetic interactions is presented. Conditions of the occurrence of phase transitions as well as the behavior of magnetization and free energy are discussed.

Physical review. B, Condensed matter•Apr 1, 1990•0 citations

Ising chains with competing interactions in the presence of long-range couplings

Alessandro Campa, Giacomo Gori, Vahan Hovhannisyan +2 more

Abstract In this paper we study an Ising spin chain with short-range competing interactions in the presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic-phase diagram. We compare our results with the limit in which one of two local interactions is turned off, which was previously studied in the literature. Eight regions of parameters with qualitatively distinct properties are featured, with different first- and second-order phase transition lines and critical points.

arXiv:1906.09668•Journal of Physics A Mathematical and Theoretical•Jul 30, 2019•15 citations

Statistical mechanics of the flexural Ising model in $D$ dimensions

Abigail Plummer

A generalization of the compressible Ising model in which spins are hosted on an elastic $D$-dimensional lattice embedded in $d>D$ dimensions is studied. Two critical systems interact when temperature is tuned to the Ising transition point, as a freely-fluctuating thermalized crystalline membrane in its flat phase is already critical. Noting that the upper critical dimension of both the membrane and Ising model is $D_{uc}=4$, renormalization group recursion relations are found by expanding in $ε=4-D$. The coupling between spin and elastic degrees of freedom is shown to be a relevant operator for the physical case of a two-dimensional membrane fluctuating in three-dimensional space ($D=2$, $d=3$), which suggests that the thermalized membrane and Ising systems become more strongly coupled at long wavelengths. The coupling is irrelevant when the difference between the space dimension and membrane dimension is greater than twelve.

arXiv:2410.01797•Oct 2, 2024•0 citations

Phase transition in a layered Ising model

A. I. Banshchikov, Yu. N. Mitsaı̆, N. V. Shakhova

The magnetization and magnetic susceptibility are calculated for a layered system in which it is assumed that the interaction between spins in a plane is long-range and only neighboring planes interact. The calculations are carried out to first order in the square of the inverse interaction radius in a plane.

Soviet Journal of Low Temperature Physics•Apr 1, 1981•0 citations
We consider two distinct ways of introducing elastic degrees of freedom in the one-dimensional Ising model. Taking into account the average effect of elastic vibrations, the effective spin Hamiltonian in the pressure ensemble diplays long-rang interactions which give rise to a first-order phase transition. However, local fluctuation of the crystalline positions lead to an effective spin Hamiltonian with short-range interactions and without any thermodynamic anomaly in one dimension.
We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions that exhibits a mixed-order transition, namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models that are seemingly unrelated. The model we present serves as a link between two classes of models that exhibit a mixed-order transition in one dimension, namely, spin models with a coupling constant that decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.
The authors consider the one-dimensional Ising model which besides the interaction of nearest neighbours includes a long-range term. The latter is ferromagnetic while the nearest-neighbour interaction can have any sign. The crossover between short- and long-range interactions when varying the Hamiltonian parameters is analysed for such a model. For some values of the antiferromagnetic short-range interaction the transition from a ferro- to paramagnetic state is of first order. At the tricritical point where the transition order changes from second to first they obtain classical tricritical exponents. For a ferromagnetic short-range interaction the Curie temperature surpasses the transition temperature of the long-range model.
Abstract In this paper we study an Ising spin chain with short-range competing interactions in the presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic-phase diagram. We compare our results with the limit in which one of two local interactions is turned off, which was previously studied in the literature. Eight regions of parameters with qualitatively distinct properties are featured, with different first- and second-order phase transition lines and critical points.
Statistical mechanics of the flexural Ising model in DDD dimensions
A generalization of the compressible Ising model in which spins are hosted on an elastic DDD-dimensional lattice embedded in d>Dd>Dd>D dimensions is studied. Two critical systems interact when temperature is tuned to the Ising transition point, as a freely-fluctuating thermalized crystalline membrane in its flat phase is already critical. Noting that the upper critical dimension of both the membrane and Ising model is Duc=4D_{uc}=4Duc​=4, renormalization group recursion relations are found by expanding in ε=4−Dε=4-Dε=4−D. The coupling between spin and elastic degrees of freedom is shown to be a relevant operator for the physical case of a two-dimensional membrane fluctuating in three-dimensional space (D=2D=2D=2, d=3d=3d=3), which suggests that the thermalized membrane and Ising systems become more strongly coupled at long wavelengths. The coupling is irrelevant when the difference between the space dimension and membrane dimension is greater than twelve.