First order transition in two dimensional coulomb glass

Abstract

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