Crystal field effects in a general S Ising spin glass

Ghatak, S.K.; Sherrington, David C.

doi:10.1088/0022-3719/10/16/023

Cited by 116 publications

(116 citation statements)

References 8 publications

Supporting

Mentioning

115

Contrasting

Order By: Relevance

“…An example of a simple disordered magnetic model presenting spontaneously IF in the mean field approximation is the Ghatak-Sherrington (GS) model 22 . The precise meaning of spontaneous existence of IF is that in this model it is not used any artificial procedure to increase the entropy of the SG phase 3 .…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2012

View full text Add to dashboard Cite

The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from GS model without RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field D, is gradually suppressed when the RF is increased.

show abstract

Section: Introductionmentioning

confidence: 99%

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

et al. 2012

View full text Add to dashboard Cite

show abstract

“…The case r = 1, namely the random exchange version of the Blume-Capel model, was first introduced and discussed by Ghatak and Sherrington (GS) [14] who used symmetric replica to obtain the relevant phase diagram. The GS solution seems to display inverse freezing even for the r = 1 case, but more detailed analysis by da Costa et.…”

mentioning

confidence: 99%

Spin Model for Inverse Melting and Inverse Glass Transition

Schupper¹,

Shnerb²

2004

Phys. Rev. Lett.

View full text Add to dashboard Cite

A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the "ferromagnetic" phase, while lower energy associated with the non-interacting states yields a "paramagnetic" phase as temperature decreases. An infinite range model is solved analytically for constant paramagnetic exchange interaction, while for its random exchange, analogous results based on the replica symmetric solution are presented. The qualitative features of this model are shown to resemble a large class of inverse melting phenomena. First and second order transition regimes are identified.PACS numbers: 05.70. Fh, 64.60.Cn, 75.10.Hk, 64.70.Pf We all tend to associate order parameter with order, namely, with less entropic microscopic realizations. This is indeed the general situation in nature: crystals are more ordered than liquids, ferromagnets have less entropy than paramagnets. Even the entropy associated with a glass, an out of equilibrium, frozen frustrated state, is less than that of a liquid phase of the same material.There are, however, exceptions, where an "order parameter" does not reflect order, and the entropy growth during crystallization or freezing. The prototype of these phenomena is inverse melting, i.e., a reversible transition between a liquid phase at low temperatures to a high temperature crystalline phase, observed in He 3 and He 4 at extreme conditions (temperature below 1 • K, pressure above 25 bar) [1]. A similar phenomenon was observed recently at room temperature and atmospheric pressure in P4MP1 polymer solutions [2]. Ferroelectricity in Rochelle salt is another example, where the spontaneous polarization is lost below the (lower) Curie temperature, this time the transition is second order in type [3]. The pinned-crystalline inverse transition of vortex lines in the presence of point disorder at high temperature superconductors [4] is also considered as an example of inverse melting. However, in that system, the intensive order parameter (bulk magnetization) is lower in the crystalline phase, and the response functions are higher, i.e., the disordered phase is stiffer than the ordered phase.Even if the crystalline state is the thermodynamically preferred one, the dynamics of the system may prevent its appearance. In glass forming materials ergodicity breaking takes place at a finite temperature and the system is trapped into a frozen disordered state. One expects that an "inverse" glass transition phenomenon, analogous to inverse melting, may also take place. An interesting example in polymeric systems is the reversible thermogelation of Methyl Cellulose solution in water [5]. When a (soft and transparent) solution of Methyl Cellulose is heated (above 50• C, for a 10 gr/liter solution) it turns into a white, turbid and mechanically strong gel. Unlike the boiling of an egg that involves an irreversible transition from a metastable to a stable state, this transition is reversible...

show abstract

“…Versions [1][2][3][4][5][6] of the Blume-Emery-Griffiths (BEG) model [7] with random interactions have been studied lately as spin models that yield thermodynamic phase diagrams exhibiting unusual reversible inverse transitions (IT), as inverse melting and inverse freezing, that have been found experimentally in a variety of quite different systems. Examples in which they occur are He 3 and He 4 isotopes at very low temperature and high pressure, the polymer P4MP1, solutions, colloidal systems, ferroelectricity in Rochelle salt, ferromagnetism of gold nanoparticles, high-temperature superconductors, and quantum-spin systems [8] (see Refs.…”

mentioning

confidence: 99%

“…The three-state spin-glass (SG) model with a crystal-field term of Ghatak and Sherrington (GS) [1] is a Blume-Capel (BC) model [10,11] with random bonds that exhibits a continuous transition between a spin-glass and a paramagnetic (P) phase at high temperature and a reentrant phase boundary at low temperature. Inverse freezing appears on the latter as a genuine thermodynamic first-order transition below a tricritical point in mean-field theory with infinite-range interactions and full replica symmetry breaking (FRSB) [3].…”

mentioning

confidence: 99%

Inverse melting and inverse freezing in a three-state spin-glass model with finite connectivity

Erichsen

2013

Phys. Rev. E

View full text Add to dashboard Cite

The phase diagrams of the three-state Ghatak-Sherrington spin-glass (or random Blume-Capel) model are obtained in mean-field theory with replica symmetry in order to study the effects of a ferromagnetic bias and finite random connectivity in which each spin is connected to a finite number of other spins. It is shown that inverse melting from a ferromagnetic to a low-temperature paramagnetic phase may appear for small but finite disorder and that inverse freezing appears for large disorder. There can also be a continuous inverse ferromagnetic to spin-glass transition. Inverse melting appears as the reversible first-order transition between a liquid or completely disordered paramagnetic phase at low temperature and a crystalline or ordered phase at higher temperature, whereas inverse freezing is the reversible first-order transition from a paramagnetic phase to a hightemperature amorphous or glassy phase [4,6]. These transitions usually appear with a reentrance in the phase boundary of continuous transitions at high temperature between an ordered and a fully disordered phase. The characteristic feature of inverse transitions is that the ordered high-temperature phase is favored by the entropy while the low-temperature disordered phase is favored by the minimum of the energy. This is best illustrated by the change of the folded into the unfolded configurations of methyl cellulose polymer chains in water. The bundles of methyl groups that are folded in a compact weakly interacting configuration at low T unfold with increasing T making more microscopic configurations available with an increase in volume and entropy [4,9].The three-state spin-glass (SG) model with a crystal-field term of Ghatak and Sherrington (GS) [1] is a Blume-Capel (BC) model [10,11] with random bonds that exhibits a continuous transition between a spin-glass and a paramagnetic (P) phase at high temperature and a reentrant phase boundary at low temperature. Inverse freezing appears on the latter as a * rubem@if.ufrgs.br † theumann@if.ufrgs.br ‡ sgmagal@gmail.com genuine thermodynamic first-order transition below a tricritical point in mean-field theory with infinite-range interactions and full replica symmetry breaking (FRSB) [3]. Similar results were obtained in mean-field theory with one-step replica symmetry breaking for the BC model with spin degeneracy [4].Inverse freezing also appears in numerical simulations for a three-dimensional GS model with nearest-neighbor interactions [6] and numerical work on the two-dimensional randombond Ising model exhibits an inverse melting transition [12]. It would be interesting to have independent analytical results for either of these random systems with finite-range interactions exhibiting both IT.Theoretical works on inverse freezing deal usually with a symmetric distribution of random bonds in fully connected systems. The purpose of the present work is to study, by means of an analytical procedure combined with a numerical evolution of a population dynamics [17], the dependence on disorder of the phase d...

show abstract

Crystal field effects in a general S Ising spin glass

Cited by 116 publications

References 8 publications

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

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

Spin Model for Inverse Melting and Inverse Glass Transition

Inverse melting and inverse freezing in a three-state spin-glass model with finite connectivity

Contact Info

Product

Resources

About