Abstract:Monte Carlo simulations have begun to illuminate the nature of phase transitions and universality classes for compressible Ising models. A comprehensive analysis of a Landau-Ginsburg Wilson hamiltonian for systems with elastic degrees of freedom predicts that there should be four cases with different behavior, depending upon symmetries and thermodynamic constraints. We shall describe the results of careful Monte Carlo simulations for a simple compressible Ising model that can be easily modified to correspond t… Show more
“…It is worth noting that the transition depends on the sample shape in hydrogen-metal systems at constant pressure 1,22 , where the proton concentration is linearly coupled to the dilation 13 . (ii) We mention Monte Carlo simulations on a binary alloy by Landau's group 10,11,12 . They assumed that a mixture undergoing unmixing corresponds to ferromagnets and that forming a superstructure to antiferromagnets.…”
Section: Summary and Concluding Remarksmentioning
confidence: 99%
“…Such elastic effects strongly depend on the nature of the coupling and their understanding is crucial in technology. In the present work, we will focus on the phase transition behavior of compressible ferromagnets or antiferromagnets, which has long been studied theoretically in the physics community 2,3,4,5,6,7,8,9,10,11,12 . In real materials, the short-range spin interactions depend on the distances among the spins, so the spin fluctuations are coupled to the elastic dilation strain.…”
Section: Introductionmentioning
confidence: 99%
“…This renormalization effect should trigger a first order phase transition sufficiently close to the critical point. Simulations have been prerformed on compressible Ising systems and a number of numerical results still remain not well understood 10,11,12 . These theories and simulations show that the phase transition depends on whether the pressure or the volume is fixed.…”
Using a Ginzburg-Landau model, we study the phase transition behavior of
compressible Ising systems at constant volume by varying the temperature $T$
and the applied magnetic field $h$. We show that two phases can coexist
macroscopically in equilibrium within a closed region in the $T$-$h$ plane. It
occurence is favored near tricriticality. We find a field-induced critical
point, where the correlation length diverges, the difference of the coexisting
two phases and the surface tension vanish, but the isothermal magnetic
susceptibility does not diverge in the mean field theory. We also investigate
phase ordering numerically.Comment: 13 figure
“…It is worth noting that the transition depends on the sample shape in hydrogen-metal systems at constant pressure 1,22 , where the proton concentration is linearly coupled to the dilation 13 . (ii) We mention Monte Carlo simulations on a binary alloy by Landau's group 10,11,12 . They assumed that a mixture undergoing unmixing corresponds to ferromagnets and that forming a superstructure to antiferromagnets.…”
Section: Summary and Concluding Remarksmentioning
confidence: 99%
“…Such elastic effects strongly depend on the nature of the coupling and their understanding is crucial in technology. In the present work, we will focus on the phase transition behavior of compressible ferromagnets or antiferromagnets, which has long been studied theoretically in the physics community 2,3,4,5,6,7,8,9,10,11,12 . In real materials, the short-range spin interactions depend on the distances among the spins, so the spin fluctuations are coupled to the elastic dilation strain.…”
Section: Introductionmentioning
confidence: 99%
“…This renormalization effect should trigger a first order phase transition sufficiently close to the critical point. Simulations have been prerformed on compressible Ising systems and a number of numerical results still remain not well understood 10,11,12 . These theories and simulations show that the phase transition depends on whether the pressure or the volume is fixed.…”
Using a Ginzburg-Landau model, we study the phase transition behavior of
compressible Ising systems at constant volume by varying the temperature $T$
and the applied magnetic field $h$. We show that two phases can coexist
macroscopically in equilibrium within a closed region in the $T$-$h$ plane. It
occurence is favored near tricriticality. We find a field-induced critical
point, where the correlation length diverges, the difference of the coexisting
two phases and the surface tension vanish, but the isothermal magnetic
susceptibility does not diverge in the mean field theory. We also investigate
phase ordering numerically.Comment: 13 figure
“…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.…”
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.
“…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 .…”
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.
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