Inverse freezing in the Ghatak-Sherrington model with a random field

Morais, C. V.; Lazo, Matheus J.; Zimmer, F.M.; Magalhães, S. G.

doi:10.1103/physreve.85.031133

Cited by 14 publications

(4 citation statements)

References 27 publications

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“…In the reentrant region the system passes from PM to CSG and then to PM. This re-entrance is similar to the unusual inverse freezing phase transition observed in non-Ising classical models [24,25], and is related to the full compensation of the total cluster spin at large negative J 0 /J. At low temperature, the fully compensated, non-magnetic cluster state is favoured.…”

Section: B Tetrahedral Clusterssupporting

confidence: 75%

Geometrical Frustration and Cluster Spin Glass with Random Graphs

Silveira,

Erichsen,

Magalhaes

2021

Preprint

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We develop a novel method based in the sparse random graph to account the interplay between geometric frustration and disorder in cluster magnetism. Our theory allows to introduce the cluster network connectivity as a controllable parameter. Two types of inner cluster geometry are considered: triangular and tetrahedral. The theory was developed for a general, non-uniform intra-cluster interactions, but in the present paper the results presented correspond to uniform, anti-ferromagnetic (AF) intra-clusters interactions J 0 /J.The clusters are represented by nodes on a finite connectivity random graph, and the inter-cluster interactions are random Gaussian distributed. The graph realizations are treated in replica theory using the formalism of order parameter functions, which allows to calculate the distribution of local fields and, as a consequence, the relevant observable.In the case of triangular cluster geometry, there is the onset of a classical Spin Liquid state at a temperature T * /J and then, a Cluster Spin Glass (CSG) phase at a temperature T f /J. The CSG ground state is robust even for very weak disorder or large negative J 0 /J. These results does not depend on the network connectivity. Nevertheless, variations in the connectivity strongly affect the level of frustration f p = −Θ CW /T f for large J 0 /J.In contrast, for the non-frustrated tetrahedral cluster geometry, the CSG ground state is suppressed for weak disorder or large negative J 0 /J. The CSG boundary phase presents a re-entrance which is dependent on the network connectivity.

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Section: B Tetrahedral Clusterssupporting

confidence: 75%

Geometrical Frustration and Cluster Spin Glass with Random Graphs

Silveira,

Erichsen,

Magalhaes

2021

Preprint

Self Cite

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“…For example, it is known that in the Gathak-Sherrington model at mean field level [7], the proper location of the first order line transition is far from obvious since the stability requirements do not provide proper guidance to select correctly the SG solution [8]. Indeed, the presence of a RF complicates the situation since the first order phase transition line is much affected by the RF [9,10]. Another aspect that should be remarked is that the RF field induces the replica symmetric SG order parameter which becomes finite at any temperature.…”

Section: Introductionmentioning

confidence: 99%

Unfolding of phases and multicritical points in the classical anisotropic van Hemmen spin glass model with random field

Magalhães

Berger

Erichsen

2019

Journal of Magnetism and Magnetic Materials

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We study magnetic properties of the 3-state spin (S i = 0 and ±1) spin glass (SG) van Hemmen model with ferromagnetic interaction J 0 under a random field (RF). The RF follows a bimodal distribution The combined effect of the crystal field D and the special type of on-site random interaction of the van Hemmen model engenders the unfolding of the SG phases for strong enough RF, i. e., instead of one SG phase, we found two SG phases. Moreover, as J 0 is finite, there is also the unfolding of the mixed phase (with the SG order parameter and the spontaneous magnetization simultaneously finite) in four distinct phases. The emergence of these new phases separated by first and second order line transitions produces a multiplication of triple and multicritical points.

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“…For this purpose, we consider the Ghatak-Sherrington (GS) model [15,16], a spin-1 SG model with a crystal field. Recently, the GS model has become well known as a prototypical model for inverse transition [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Inverse transitions in a spin-glass model on a scale-free network

Kim

2014

Phys. Rev. E

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In this paper, we will investigate critical phenomena by considering a model spin glass on scale-free networks. For this purpose, we consider the Ghatak-Sherrington (GS) model, a spin-1 spin-glass model with a crystal field, instead of the usual Ising-type model. Scale-free networks on which the GS model is placed are constructed from the static model, in which the number of vertices is fixed from the beginning. On the basis of the replica-symmetric solution, we obtain the analytical solutions, i.e., free energy and order parameters, and we derive the various phase diagrams consisting of the paramagnetic, ferromagnetic, and spin-glass phases as functions of temperature T, the degree exponent λ, the mean degree K, and the fraction of the ferromagnetic interactions ρ. Since the present model is based on the GS model, which considers the three states (S = 0, ± 1), the S = 0 state plays a crucial role in the λ-dependent critical behavior: glass transition temperature T(g) has a finite value, even when 2 < λ < 3. In addition, when the crystal field becomes nonzero, the present model clearly exhibits three types of inverse transitions, which occur when an ordered phase is more entropic than a disordered one.

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Inverse freezing in the Ghatak-Sherrington model with a random field

Cited by 14 publications

References 27 publications

Geometrical Frustration and Cluster Spin Glass with Random Graphs

Geometrical Frustration and Cluster Spin Glass with Random Graphs

Unfolding of phases and multicritical points in the classical anisotropic van Hemmen spin glass model with random field

Inverse transitions in a spin-glass model on a scale-free network

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