Numerical Evidence for Critical Behavior of the Two-Dimensional Nonequilibrium Zero-Temperature Random Field Ising Model

Spasojević, Djordje; Janićević, Sanja; Knežević, Milan

doi:10.1103/physrevlett.106.175701

Cited by 64 publications

(62 citation statements)

References 18 publications

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“…From the standard picture [19][20][21][22] one finds that the transition is second order, but there are few arguments in support of first order transition as well [23][24][25][26] . Recent work on 2d RFIM [27][28][29][30] also claim presence of ordered state in the system at finite disorder, but the nature of transition is not clear. In our previous work 6 , we have given an argument that for a compact domain, the energy of formation of domain in CG system also scales as L d−1 .…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of the two-dimensional Coulomb glass at zero temperature

2017

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The lattice model of Coulomb Glass in two dimensions with box-type random field distribution is studied at zero temperature for system size upto 96 2 . To obtain the minimum energy state we annealed the system using Monte Carlo simulation followed by further minimization using clusterflipping. The values of the critical exponents are determined using the standard finite size scaling. We found that the correlation length ξ diverges with an exponent ν = 1.0 at the critical disorder Wc = 0.2253 and that χ dis ≈ ξ 4−η withη = 2 for the disconnected susceptibility. The staggered magnetization behaves discontinuously around the transition and the critical exponent of magnetization β = 0. The probability distribution of the staggered magnetization shows a three peak structure which is a characteristic feature for the phase coexistence at first-order phase transition. In addition to this, at the critical disorder we have also studied the properties of the domain for different system sizes. In contradiction with the Imry-Ma arguments, we found pinned and noncompact domains where most of the random field energy was contained in the domain wall. Our results are also inconsistent with Binder's roughening picture.

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Section: Introductionmentioning

confidence: 99%

Critical behavior of the two-dimensional Coulomb glass at zero temperature

2017

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“…Recently, Spasojevic et.al. [9] gave numerical evidence that the 2d non equilibrium zero-temperature RFIM exhibits a critical behaviour. The Hamiltonian for such a * suman.sinha.phys@gmail.com † pradipta.mandal@gmail.com system is, in general, given by…”

Section: Introductionmentioning

confidence: 99%

Dynamical properties of random-field Ising model

Sinha

Mandal²

2013

Phys. Rev. E

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Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter and the spin-spin correlation functions are studied in the non equilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two dimensional random field Ising model possesses long range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long range order in the system.

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“…In 2012, Aizenmann [9] too claims existence of phase transition in 2d RFIM. Spasojevic et al [10] have also given some numerical evidences which proves the existence of phase transition in 2d nonequilibrium RFIM at T = 0. Recently, Suman and Mandal [11] have studied some aspects of nonequilibrium 2d RFIM at low temperature.…”

Section: Introductionmentioning

confidence: 87%

First order transition in two dimensional coulomb glass

Bhandari

Malik

2017

J. Phys.: Conf. Ser.

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Abstract.We have studied the ground states of two dimensional lattice model of Coulomb Glass via Monte Carlo annealing. Our results show a possibility of existence of a critical disorder (W c ) below which the system is in the charge ordered phase and above it the system is in the disordered phase. We have used finite size scaling to calculate W c = 0.2413, the critical exponent of magnetization β = 0 indicating discontinuity in magnetization and the critical exponent of correlation length ν = 1.0. The distribution of staggered magnetization for different disorder strengths shows a three peak structure. We thus predict that two dimensional Coulomb Glass shows a first order transition at T=0. IntroductionSince the introduction of Random field Ising Model, a lot of discussion has been done on the possibility of existence of ferromagnetic ordering below a critical disorder strength (W c ) in two dimensional (2D) RFIM. From Imry-Ma arguments [1], one finds that the lower critical dimension (d c ) below which the ferromagnetic ordered phase gets destroyed is d c ≤ 2, where d = 2 was considered as a limiting case. By doing field theoretical calculations [2,3], later it was suggested that d c = 3. In 1983, Binder [4] gave an argument that the roughening of domain walls would lead to the destruction of ferromagnetic ordering in 2d RFIM. Then an exact result was given by Bricmont and Kupiainen [5] in 1987 where they showed that there exist a ferromagnetic ordering in three dimensional (3d) RFIM. A rigorous theoretical proof was then given by Aizenman and Wehr [6] in 1989 that no long range ordering is possible in 2d RFIM case. Scaling theory for 3d RFIM assuming second order transition at T=0 leads to modified hyperscaling laws [7]. However, in contradiction to all the above arguments Frontera and Vives [8] in 1999 showed numerical signs of transition in 2d RFIM at zero temperature below a critical random field strength. In 2012, Aizenmann [9] too claims existence of phase transition in 2d RFIM. Spasojevic et al [10] have also given some numerical evidences which proves the existence of phase transition in 2d nonequilibrium RFIM at T = 0. Recently, Suman and Mandal [11] have studied some aspects of nonequilibrium 2d RFIM at low temperature. They have commented that 2d RFIM exhibits a phase transition in the disorder parameter even at T > 0. These numerical work suggests a possibility of presence of long range ordering in 2d RFIM at low disorder strengths. If we assume that the above arguments which are claiming that at T = 0 there is a finite disorder strength below which long range ordering in 2d RFIM exist, then the order of transition is another question which is not answered very clearly. This question remains unclear even for 3d RFIM where there is no controversy over the presence of phase transition at zero temperature. Some earlier work suggested a first order transition [12][13][14][15][16][17][18] but there are arguments [19][20][21][22] which favour second order

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Numerical Evidence for Critical Behavior of the Two-Dimensional Nonequilibrium Zero-Temperature Random Field Ising Model

Cited by 64 publications

References 18 publications

Critical behavior of the two-dimensional Coulomb glass at zero temperature

Critical behavior of the two-dimensional Coulomb glass at zero temperature

Dynamical properties of random-field Ising model

First order transition in two dimensional coulomb glass

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