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

Journal of Physics A Mathematical and General

Axial decorated Ising model with competing interaction

Roberto J. V. dos Santos, S. Coutinho, J. R. L. de Almeida

Published Oct 21, 1986• 12 citations
Publisher

Abstract

The phase diagram and the thermodynamics of the axial decorated Ising model on a square lattice with m-dimensional bond spins are studied for the m=1 (Ising), m=2 (XY), m=3 (Heisenberg) and m= infinity cases. Competing interactions between the site and decorating bond spins have been considered. The expressions for the partition function, the thermodynamics and the pair correlation functions of the decorated Ising chain have been analytically obtained. The effect of the dimensionality of the decorating bond spin on the thermodynamic behaviour of both models is analyzed.

DOI
10.1088/0305-4470/19/15/027

Related papers

Multiple re-entrant phenomenon on decorated square lattice Ising models

Roberto J. V. dos Santos, F. C. Sá Barreto, S. Coutinho

The re-entrant phenomenon is studied in the antiferromagnetic Ising model on a square lattice with the bonds decorated with two and three-coupled spin 1/2 variables (dimer and trimer) in two different scenarios. In the first one ferromagnetic competing decorated bonds are anneal diluted in the system. The exact phase diagrams of the critical temperature as a function of the concentration and of the competition parameter are obtained. In contrast to the single spin bond decoration, a double re-entrant behaviour is observed. The bond percolation threshold P c =(1-1/2)/2 is achieved and it is independent of the decorating variable. In the second scenario the pure axial decorated system is studied. The analytical temperature against competition parameter phase diagram and the specific heat are calculated and discussed. In this latter case multiple re-entrances are observed for a certain range of the competition parameter. The nature of this re-entrant phenomenon is discussed.

Journal of Physics A Mathematical and General•Jun 21, 1990•7 citations

Exactly soluble Ising models exhibiting multiphase points

David A. Huse, Julia M. Yeomans, Michael Ellis Fisher

A class of decorated spin 1/2 Ising models is introduced: all bonds of a hypercubic lattice parallel to one axis are decorated by n spins. Within each decorated bond, nearest neighbor ferromagnetic interactions compete with next-nearest neighbor antiferromagnetic interactions. An exact dedecoration transformation reduces the model to an anisotropic Ising model which is exactly soluble in two dimensions (d = 2) and for which accurate series expansion estimates are available for d = 3. Phase diagrams are presented for d = 2 and 3 : all exhibit a multiphase point at which many distinct, spatially modulated commensurate phases coexist. The variation of the characteristic wavevector and other properties are compared and contrasted with those of the axial next-nearest neighbor Ising (ANNNI) models.

Journal of Applied Physics•Mar 1, 1981•2 citations

Decorated Ising model in a magnetic field

L.L. Gonçalves, Tomoya Horiguchi

A study of the two-dimensional Ising model on a rectangular lattice decorated with v-dimensional classical vector spins or Ising spins of magnitude s in an external field is presented. Exact expressions are obtained for the magnetisation and correlation functions, and the phase diagram is also determined exactly. It is shown that when there is no direct interaction between the spins of the host lattice there is a critical field h c , above which the system does not present long range order, and that this h c does not depend on v or s. The isothermal susceptibility related to the decorating spins is also obtained exactly, and it is shown that it diverges logarithmically at the transition temperature only for non-vanishing external field. A discussion is presented on the solution of equivalent models, and as a by-product it is shown how to map the model onto the two-dimensional eight-vertex model with temperature dependent parameters in an arbitrary staggered field.

Journal of Physics A Mathematical and General•Jun 1, 1986•10 citations

Phase Diagram and Ground State of a Decorated Ising Model on a Cubic Lattice

Vadim A. Mutailamov, Akai Kurbanovich Murtazaev

Abstract The static critical behavior of a three-dimensional decorated Ising model on a cubic lattice is investigated by the methods of computational physics. The case is considered when the exchange interaction Jn = –1 between nodal spins is antiferromagnetic and the interaction Jd between nodal spins and decorated spins varies within [–3.0; 3.0]. For various values of Jd, the ground state of the model is determined, the critical temperatures and critical exponents are calculated, and the phase diagram is constructed. It is shown that, for any ratios of exchange interactions in the model, a second-order phase transition is observed from an ordered to a paramagnetic state, and the critical exponents are close to the values for the standard Ising model.

Journal of Experimental and Theoretical Physics•Jul 1, 2021•6 citations

Crossed Ising chains: a special decorated two-dimensional Ising model showing a transition to first-order behaviour

K Jungling, Gustav M. Obermair

A system of crossed Ising chains that can be interpreted as a multiply decorated square Ising lattice is considered and the local spontaneous magnetization which 'hangs through' between the crossing points is discussed. With growing chain distance the coupling constant along the decorated horizontal bonds is allowed to increase such that the critical temperature of the second-order transition remains constant. A narrowing of the critical region with increasing chain distance is observed; in the limit of infinite distance spontaneous magnetization, specific heat and susceptibility exhibit a first-order transition. Thus the model serves as an example for the continuous variation of the character of a phase transition from second to first kind as a function of the 'external parameter' chain distance.

Journal of Physics C Solid State Physics•Mar 7, 1975•2 citations

Phase diagram of the asymmetric tetrahedral Ising–Heisenberg chain

J. S. Valverde, Onofre Rojas, S. M. de Souza

The asymmetric tetrahedron is composed of all edges of a tetrahedron represented by Ising interactions except for one, which has a Heisenberg-type interaction. This asymmetric tetrahedron is arranged by connecting a vertex whose edges are only Ising-type interactions to another vertex with the same structure for another tetrahedron. The process is replicated and this kind of lattice we call the asymmetric Ising–Heisenberg chain. We have studied the ground-state phase diagram for this kind of model. In particular, we consider two situations in the Heisenberg-type interaction: (i) the asymmetric tetrahedral spin-(1/2, 1/2) Ising-XYZ chain and (ii) the asymmetric tetrahedral spin-(1/2, 1) Ising-XXZ chain, where we have found a rich phase diagram and a number of multicritical points. Additionally we have also studied their thermodynamical properties and the correlation function, using the decorated transformation. We have mapped the asymmetric tetrahedral Ising–Heisenberg chain in an effective Ising chain, and we have also concluded that it is possible to evaluate the partition function including a longitudinal external magnetic field.

arXiv:0807.4796•Journal of Physics Condensed Matter•Aug 1, 2008•47 citations
The phase diagram and the thermodynamics of the axial decorated Ising model on a square lattice with m-dimensional bond spins are studied for the m=1 (Ising), m=2 (XY), m=3 (Heisenberg) and m= infinity cases. Competing interactions between the site and decorating bond spins have been considered. The expressions for the partition function, the thermodynamics and the pair correlation functions of the decorated Ising chain have been analytically obtained. The effect of the dimensionality of the decorating bond spin on the thermodynamic behaviour of both models is analyzed.
The re-entrant phenomenon is studied in the antiferromagnetic Ising model on a square lattice with the bonds decorated with two and three-coupled spin 1/2 variables (dimer and trimer) in two different scenarios. In the first one ferromagnetic competing decorated bonds are anneal diluted in the system. The exact phase diagrams of the critical temperature as a function of the concentration and of the competition parameter are obtained. In contrast to the single spin bond decoration, a double re-entrant behaviour is observed. The bond percolation threshold P c =(1-1/2)/2 is achieved and it is independent of the decorating variable. In the second scenario the pure axial decorated system is studied. The analytical temperature against competition parameter phase diagram and the specific heat are calculated and discussed. In this latter case multiple re-entrances are observed for a certain range of the competition parameter. The nature of this re-entrant phenomenon is discussed.
A class of decorated spin 1/2 Ising models is introduced: all bonds of a hypercubic lattice parallel to one axis are decorated by n spins. Within each decorated bond, nearest neighbor ferromagnetic interactions compete with next-nearest neighbor antiferromagnetic interactions. An exact dedecoration transformation reduces the model to an anisotropic Ising model which is exactly soluble in two dimensions (d = 2) and for which accurate series expansion estimates are available for d = 3. Phase diagrams are presented for d = 2 and 3 : all exhibit a multiphase point at which many distinct, spatially modulated commensurate phases coexist. The variation of the characteristic wavevector and other properties are compared and contrasted with those of the axial next-nearest neighbor Ising (ANNNI) models.
A study of the two-dimensional Ising model on a rectangular lattice decorated with v-dimensional classical vector spins or Ising spins of magnitude s in an external field is presented. Exact expressions are obtained for the magnetisation and correlation functions, and the phase diagram is also determined exactly. It is shown that when there is no direct interaction between the spins of the host lattice there is a critical field h c , above which the system does not present long range order, and that this h c does not depend on v or s. The isothermal susceptibility related to the decorating spins is also obtained exactly, and it is shown that it diverges logarithmically at the transition temperature only for non-vanishing external field. A discussion is presented on the solution of equivalent models, and as a by-product it is shown how to map the model onto the two-dimensional eight-vertex model with temperature dependent parameters in an arbitrary staggered field.
Abstract The static critical behavior of a three-dimensional decorated Ising model on a cubic lattice is investigated by the methods of computational physics. The case is considered when the exchange interaction Jn = –1 between nodal spins is antiferromagnetic and the interaction Jd between nodal spins and decorated spins varies within [–3.0; 3.0]. For various values of Jd, the ground state of the model is determined, the critical temperatures and critical exponents are calculated, and the phase diagram is constructed. It is shown that, for any ratios of exchange interactions in the model, a second-order phase transition is observed from an ordered to a paramagnetic state, and the critical exponents are close to the values for the standard Ising model.
A system of crossed Ising chains that can be interpreted as a multiply decorated square Ising lattice is considered and the local spontaneous magnetization which 'hangs through' between the crossing points is discussed. With growing chain distance the coupling constant along the decorated horizontal bonds is allowed to increase such that the critical temperature of the second-order transition remains constant. A narrowing of the critical region with increasing chain distance is observed; in the limit of infinite distance spontaneous magnetization, specific heat and susceptibility exhibit a first-order transition. Thus the model serves as an example for the continuous variation of the character of a phase transition from second to first kind as a function of the 'external parameter' chain distance.
The asymmetric tetrahedron is composed of all edges of a tetrahedron represented by Ising interactions except for one, which has a Heisenberg-type interaction. This asymmetric tetrahedron is arranged by connecting a vertex whose edges are only Ising-type interactions to another vertex with the same structure for another tetrahedron. The process is replicated and this kind of lattice we call the asymmetric Ising–Heisenberg chain. We have studied the ground-state phase diagram for this kind of model. In particular, we consider two situations in the Heisenberg-type interaction: (i) the asymmetric tetrahedral spin-(1/2, 1/2) Ising-XYZ chain and (ii) the asymmetric tetrahedral spin-(1/2, 1) Ising-XXZ chain, where we have found a rich phase diagram and a number of multicritical points. Additionally we have also studied their thermodynamical properties and the correlation function, using the decorated transformation. We have mapped the asymmetric tetrahedral Ising–Heisenberg chain in an effective Ising chain, and we have also concluded that it is possible to evaluate the partition function including a longitudinal external magnetic field.