Compressible Ising spin glass: Simulation results

Marshall, Adam H.

doi:10.1103/physrevb.75.054414

Cited by 5 publications

(6 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The presence of ν brings neighboring energy levels closer together in energy, and the large-ν simulations equilibrate rapidly. We find that the L-dependence of the simulations is somewhat trivial: when scaled by the number of particles, computed quantities converge quickly to asymptotic values as L increases [19].…”

mentioning

confidence: 86%

See 1 more Smart Citation

Numerical studies of the compressible Ising spin glass

2006

View full text Add to dashboard Cite

We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with ±J interactions. We find that the energy of a given spin configuration is shifted from its incompressible value, E0, by an amount quadratic in E0 and proportional to the coupling strength. We then construct a simple model expressed only in terms of spin variables that predicts the existence of a critical value of the coupling above which the spin-glass transition disappears.PACS numbers: 75.10. Nr,75.40.Mg,05.50.+q Lattice compressibility affects the nature of phase transitions in a variety of spin systems. The 2-dimensional (2-D) triangular Ising antiferromagnet, for example, is fully frustrated and shows no transition to an ordered state; however, when compressibility is added, this system exhibits a first-order transition to a striped phase [1,2]. In the (unfrustrated) Ising ferromagnet, the introduction of compressibility changes the transition from second-to first-order so that the onset of nonzero net magnetization is simultaneous with a discontinuous change in the volume [3,4]. Frustration is central to the nature of the spin-glass transition as it leads to large ground-state degeneracies [5,6,7,8]. Because different states with the same spin-glass energy can couple differently to local lattice deformations, compressibility lifts the ground-state degeneracy and may dramatically alter the nature of the transition and the low-temperature spin-glass phase. Since magneto-elastic effects are always present to some degree in physical systems, their inclusion in spin-glass models may help explain some of the outstanding puzzles in spin-glass experiments [9]. We report here the effect of compressibility on a 2-D spin glass in which the lattice is allowed to distort locally while the entire system is held at constant volume.The ground states of the previously studied compressible systems were always states that had already been ground states of those same systems without lattice distortion. In contrast, we find that as the coupling between magnetic interactions and lattice distortions is increased, the constant-volume compressible spin glass prefers spin configurations which had previously been excited states. We further find that the critical region just above the spin-glass temperature is suppressed as the coupling to lattice distortions increases so that above a certain value of the coupling, the spin-glass transition is eliminated entirely.We study compressible two-dimensional Ising spin glasses on square lattices with periodic boundary conditions at constant volume. The Hamiltonian isThe first term is the energy of the standard (incompressible) Edwards-Anderson spin glass, with a sum over nearest neighbors. The spins S i take the values ±1, and J ij ∈ {±J}. The second term couples the spin interactions to local lattice distortions; r ij is the distance between particles i and j, and r 0 is the particle separation of t...

show abstract

mentioning

confidence: 86%

“…The entropy of the ±J spin glass is well described by a quadratic with hyperbolic cosine corrections [19]:…”

mentioning

confidence: 99%

Numerical studies of the compressible Ising spin glass

2006

View full text Add to dashboard Cite

show abstract

“…Although elastic spin models with uniform interactions have been much investigated, disordered compressible spin models are less explored. Nowadays it has been feasible to carry out detailed computer simulations for compressible models [15,16,17], including disordered compressible models, as in the work of Marshall for a compressible Edwards-Anderson Ising spin-glass on a two-dimensional lattice [18,19]. These works have provided further motivation to study the phase diagram of the simple compressible SK spin-glass model.…”

Section: Introductionmentioning

confidence: 99%

Compressible Sherrington-Kirkpatrick spin-glass model

Liarte,

Salinas,

Yokoi

2008

Preprint

View full text Add to dashboard Cite

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressuretemperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The secondorder para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperatureconcentration phase diagrams of mixtures of hydrogen-bonded crystals.

show abstract

“…Chamamos a atenção para o fato de que simulações numéricas com alta precisão de modelos compressíveis tornaram-se possíveis apenas recentemente, com o aumento da capacidade de processamento dos computadores modernos e o desenvolvimento de algoritmos mais eficazes (Mitchell, Pereira, e Landau, 2008). Aqui também servem de paradigma os modelos de Ising compressíveis com interações ferro (Landau, 2006) (Marshall, Chacraborty, e Nagel, 2006;Marshall, 2007), não há relatos na literatura sobre estudos de modelos compressíveis a partir de abordagens analíticas 12 .…”

Section: O Problema Físicounclassified

Modelos estatísticos de campo médio para vidros de spins e fluidos complexos

Paulo¹,

Liarte²

View full text Add to dashboard Cite

A minha família, em especial aos meus pais Antônio e Francisca, meus irmãos Sélia, Alan, Jardilson, Daniel e David, minha irmã na criação Francisca, meus tantos sobrinhos e minha querida noiva, Thais, pelo incomensurável apoio, carinho e exemplo, fontes de contínua inspiração. Ao meu orientador, Prof. Carlos Yokoi, ao meu coorientador, Prof. Silvio Roberto Salinas, e ao Prof. José Pimentel de Lima, educadores formidáveis a quem devo orientação, supervisão, assim como tantas conversas estimulantes. Aos amigos e colegas, dentro e fora da vida acadêmica. A vários dos professores da Universidade Federal do Piauí e da Universidade de São Paulo, pelo auxílio na formação acadêmica. Aos Profs. Carlos Eugênio, Tânia Tomé e Vera Henriques, pelas sugestões e dúvidas apresentadas no meu exame de qualificação.

show abstract

Compressible Ising spin glass: Simulation results

Cited by 5 publications

References 33 publications

Numerical studies of the compressible Ising spin glass

Numerical studies of the compressible Ising spin glass

Compressible Sherrington-Kirkpatrick spin-glass model

Modelos estatísticos de campo médio para vidros de spins e fluidos complexos

Contact Info

Product

Resources

About