Exact results for the temperature-field behavior of the Ginzburg-Landau Ising type mean-field model

TL;DR

This paper derives exact analytical results for the behavior of the order parameter and susceptibilities in a mean-field Ginzburg-Landau Ising model with film geometry, revealing novel phase transition phenomena and susceptibility profiles.

Contribution

It provides the first exact analytical expressions for the scaling functions of order parameter and susceptibilities in this model, including novel insights into capillary condensation behavior.

Findings

Existence of a pre-critical jump in density below bulk critical temperature.

Susceptibility profiles with one or two maxima depending on phase coexistence.

Exact analytical expressions for scaling functions in the model.

Abstract

We investigate the dependence of the order parameter profile, local and total susceptibilities on both the temperature and external magnetic field within the mean-filed Ginzburg-Landau Ising type model. We study the case of a film geometry when the boundaries of the film exhibit strong adsorption to one of the phases (components) of the system. We do that using general scaling arguments and deriving exact analytical results for the corresponding scaling functions of these quantities. In addition, we examine their behavior in the capillary condensation regime. Based on the derived exact analytical expressions we obtained an unexpected result -- the existence of a region in the phase transitions line where the system jumps below its bulk critical temperature from a less dense gas to a more dense gas before switching on continuously into the usual jump from gas to liquid state in the middle of the system. It is also demonstrated that on the capillary condensation line one of the coexisting local susceptibility profiles is with one maximum, whereas the other one is with two local maxima centered, approximately, around the two gas-liquid interfaces in the system.