Near-equilibrium dynamics of the random field Ising model

Abstract This study examines the relaxation dynamics of the random field Ising model within a phenomenological framework based on irreversible thermodynamics. A small, uniform external field is applied for a short duration, then suddenly turned off, to monitor the ensuing relaxation of the Ising model under the influence of a longitudinal random field with a distinct bimodal distribution. The mean-field phase diagram is obtained by combining the Landau expansion of the free energy with numerical evaluations of the equations of state. The study shows that the temperature variance of the relaxation time ( $$\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> </mml:math> ) exhibits singularity near second-order and tricritical points, indicating the well-known critical slowing down phenomena. The relaxation time $$\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> </mml:math> exhibits finite and discontinuous jumps, which is a clear signature of the bimodal random field forcing the system into an abrupt structural shift near a discontinuous phase transition. The critical and tricritical exponents, along with their associated amplitudes, are determined to characterize the system’s critical behavior further. A rise in critical amplitude near the tricritical point shows a “flattened” free-energy landscape. This makes the system more sensitive to quenched disorder. The temperature variation of $$\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> </mml:math> reveals the coupled nature of disorder, criticality, and relaxation dynamics in the RFIM.