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Schmittmann, Beate; Zia, R. K. P.

doi:10.1023/a:1023069325518

Cited by 13 publications

(15 citation statements)

References 9 publications

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“…This method can certainly be extended to our anisotropic system. Another route to an estimate of the shift of T c is based on a recent study of the two-point correlation function G(x) in a "high temperature" expansion [10], which is actually an expansion in small J or K = J/k B T . In this approach, an approximate equation for G(x), first derived in [9] is solved exactly.…”

Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

“…In this approach, an approximate equation for G(x), first derived in [9] is solved exactly. The resultant Fourier transform is just the theoretical structure factor: S(k) which not only displays the well understood discontinuity singularity at k = 0 [22], but also may be exploited to estimate T c (E) [10]. The results are less accurate than those from dynamic mean-field theory, since the latter is the generalization of the Bethe-Peierls approximation for equilibrium Ising models.…”

Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

“…Here, we provide a brief presentation of the generalization to the anisotropic model. With reference to [9,10], where the derivation and the nature of the approximation can be found, we simply quote the equation for G :…”

Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

“…Since α does not affect the structure of these equations and enters only through the inhomogeneous terms, we can follow the analysis in [10] closely and obtain the equation for T c (α, E). The result can be succinctly summarized by…”

Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

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Shaw

Schmittmann

Zia

1999

Journal of Statistical Physics

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The Ising lattice gas, with its well known equilibrium properties, displays a number of surprising phenomena when driven into non-equilibrium steady states. We study such a model with anisotropic interparticle interactions ( J = J ⊥ ), using both Monte Carlo simulations and high temperature series techniques. Under saturation drive, the shift in the transition temperature can be both positive and negative, depending on the ratio J /J ⊥ ! For finite drives, both first and second order transitions are observed. Some aspects of the phase diagram can be predicted by investigating the two point correlation function at the first non-trivial order of a high temperature series expansion.

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Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

Section: Two Point Correlation In a High Temperature Expansionmentioning

confidence: 99%

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Shaw

Schmittmann

Zia

1999

Journal of Statistical Physics

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“…Field-theoretical studies have indicated that the effects of nonequilibrium dynamics are drastic in systems where detailed balance violation is coupled with conserved anisotropic dynamics [1]. In these systems, effective long range interactions can be induced by the local dynamics producing a critical behavior that is remarkably different from the one of the corresponding unperturbed, equilibrium, systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].In this paper, we present the phase diagram for a two-dimensional two-temperature diffusive conserved order parameter XY model. The system evolves through Kawasaki spin-exchange dynamics [19].…”

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Phase diagram for a two-dimensional, two-temperature, diffusiveXYmodel

2010

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Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature conserved order parameter XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow from the higher temperature heat-bath to the lower temperature one and reaches a far-fromequilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin texture order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent ϕ = 2.52 ± 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point. Much of the research in the statistical physics of nonequilibrium sytems has been directed toward understanding how universal equilibrium critical phenomena are affected by dynamical nonequilibrium perturbations. Field-theoretical studies have indicated that the effects of nonequilibrium dynamics are drastic in systems where detailed balance violation is coupled with conserved anisotropic dynamics [1]. In these systems, effective long range interactions can be induced by the local dynamics producing a critical behavior that is remarkably different from the one of the corresponding unperturbed, equilibrium, systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].In this paper, we present the phase diagram for a two-dimensional two-temperature diffusive conserved order parameter XY model. The system evolves through Kawasaki spin-exchange dynamics [19]. Thus, the dynamics is purely relaxational with no reversible mode couplings, and corresponds to Model B of Ref. 20. Long range order can exist in nonequilibrium steady states of this system due to the effective long range interactions generated by the anisotropic diffusive dynamics that occurs in that regime. The ordered phase is characterized by the appearance of standing spin waves, or spin textures, oriented along the direction of lower temperature. The system exhibits a nonequilibrium disorderlong-range order transition that is in the same universality class as an equilibrium model with dipole interactions [11,14]. Note that our model reduces to the equilibrium XY model in the limit where both temperatures are equal. Also, the Mermin-Wagner theorem states that there is no spontaneous symmetry breaking in equilibrium systems with continuous symmetry of * Present address: Max Planck Institut für Physik complexer Systeme, Nöthnitzerstraße 38, 01187 Dresden, Germany.the order parameter and dimension d = 2 [21]. Thus, no long-range ordered phase is observed in the tw...

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Driven Diffusive Systems: a Tutorial and Recent Developments

Zia

2003

Computer Simulations of Surfaces and Interfaces

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Cited by 13 publications

References 9 publications

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Phase diagram for a two-dimensional, two-temperature, diffusiveXYmodel

Driven Diffusive Systems: a Tutorial and Recent Developments

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