Heisenberg model in a random field: phase diagram and tricritical behavior

Abstract

By using the differential operator technique and the effective field theory scheme we study the tricritical behavior of Heisenberg classical model of spin-1/2 in a random field. The phase diagram in the T-h plane on a square and simple cubic lattice for a cluster with two spins is obtained when the random field is bimodal distributed. : 71.28+d, 71.30+h, 72.10-d. PACS

Phase diagram and tricritical behavior of an metamagnet in uniform and random fields

“…In particular, there is still room to investigate the existence of a tricritical point [5,6] and the exact relation to the dilute antiferromagnet in a uniform field. Depending on the choice of the random-field distribution, the mean-field approximation gives rise to a tricritical point (which is present for a symmetric double-d distribution [7], but does not occur in the case of a Gaussian form [8]).…”

Absence of tricritical behavior of the random field Ising model in a honyecomb lattice

“…In last years, the random field Ising model (RFIM) has been investigated extensively both theoretically and experimentally [1][2][3][4][5]. The problem of the RFIM which, was introduced by Imry and Ma [2], has become the subject of experimental and theoretical interest [3].…”

“…The problem of the RFIM which, was introduced by Imry and Ma [2], has become the subject of experimental and theoretical interest [3]. Many theoretical problems associated with the ferromagnetic RFIM have been studied extensively by several authors [1,3,4,6,7], such as phase transitions and critical behavior. Within the framework of the mean field approximation, it is well-known that the bimodal random field distribution leads to a tricritical behavior, but the Gaussian distribution only exhibits a second order phase transition.…”

“…In particular, the renormalization group theory (RG) of phase transitions and critical phenomena represents one of the most powerful tools of theoretical physics in last decades. By employing the same strategy of RG, the effective field theory (EFT) has been used to study cooperative phenomena and phase transitions in various systems and giving useful qualitative and quantitative insights for the critical behavior of a wide variety of classical [4,[16][17][18][19][20] and quantum lattice [21,22] spin systems. In the present letter, we study the RFIM within a scheme of the EFT method, including the contribution of the set of spins which are chosen in a systematic way by increasing the number of surrounding spins (see Fig.…”

Monte Carlo study of the metamagnet Ising model in a random and uniform field

“…On the other hand, questions such as the lower critical dimension [5,6] and the existence of a static phase transition have already been solved from the theoretical point of view. However, questions such as the existence of the tricritical point [7][8][9][10][11] are still open. The relevance of RFIM is due to the fact that it is the simplest model used to describe the essential physics of a rich class of experimentally accessible disordered systems, which includes: i) structural phase transitions in random alloys [12], ii) commensurate chargedensity-wave systems with impurity pinning [13,14], iii) binary fluid mixtures in random porous media [15], iv) melting of intercalates in layered compounds such as T i S 2 [16], v) frustration introduced by the disorder in interacting many body systems, besides explaining several aspects of electronic transport in disordered insulators [17] and vi) systems near the metal-insulator transition [18,19].…”