Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

Abstract

The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered, respectively, at +H0 and -H0, presenting the same width sigma . It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well-known limits, namely, the single Gaussian distribution (sigma>>H0) and the bimodal one (sigma=0) . The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution. Critical frontiers exhibiting tricritical points occur for different values of sigma , with the possibility of two tricritical points along the same critical frontier. To our knowledge, it is the first time that such a behavior is verified for a spin-glass model in the presence of a continuous-distribution random field, which represents a typical situation of a real system. The stability of the replica-symmetric solution is analyzed, and the usual Almeida-Thouless instability is verified for low temperatures. It is verified that the higher-temperature tricritical point always appears in the region of stability of the replica-symmetric solution; a condition involving the parameters H0 and sigma , for the occurrence of this tricritical point only, is obtained analytically. Some of our results are discussed in view of experimental measurements available in the literature.

The random-field Ising model with asymmetric bimodal probability distribution

“…The SOPT boundary is determined by setting A = 1 and C < 0, whereas for the FOPT boundary by A = 1 and C > 0 [6-9,12,18,23]. These two boundaries, whenever they coexist, are joined at a tricritical point determined by the condition A = 1 and C = 0 [6][7][8][9]12,36,37,18,23], provided that E < 0 (equivalently, F 6 < 0) as in Refs. [36,37].…”

“…The value ω 1 = 0 (two-fold) is again a solution or, equivalently, M 1 = 0 (PM phase); the other three ones are the solutions to the equation, = q 3 + r 2 ≥ 0 (r = −30F 3 /F 6 , q = (20F 4 )/(3F 6 )), namely, (36) or three real ones for < 0, that is,…”

The random field Ising model with an asymmetric trimodal probability distribution

“…The SOPT boundary is determined by setting A = 1 and C < 0, whereas the FOPT boundary by A = 1 and C > 0. These two boundaries, whenever appear sequentially, are joined at a tricritical point determined by the condition A = 1 and C = 0 [8,20,21,22,26,36,37,38], provided that E < 0 (equivalently, F 6 < 0) for stability, as also in [36,37]. However, for the FOPT boundary we shall use, in addition to (12) and (14), the requirement of the equality of the respective free energies, ) are calculated as functions of the probabilities p, q.…”

Thermodynamics, dielectric permittivity and phase diagrams of the Rb_{1-x}(NH_{4})_{x}H_{2}PO_{4} type proton glasses

“…If in (1.1) the distribution function of the fields h i consists of two Gaussians, then a critical point appears on the phase boundary between the ferroelectric and paraelectric phases, whereas the transition between the ferroelectric and paraelectric phases becomes the first order one [70].…”