Critical specific heat of systems confined by a wall

Z. Borjan

Physica A: Statistical Mechanics and its Applications, 2022, vol. 594, issue C

Abstract: We analyze quantitatively the surface (excess) specific heat near criticality for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a planar wall belonging to the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. In order to determine the universal surface amplitudes and the spatially varying scaling functions which govern the behavior of the specific heat we use the local-functional theory. Our analysis pertains to the critical isochore, near two-phase coexistence, and along the critical isotherm if (in magnetic language) the surface and the weak bulk magnetic fields are either collinear or anti-collinear. The universal scaling functions which underly calculations of the specific heat are monotonic in most cases, except along the critical isotherm for anti-collinear bulk and surface magnetic fields. Among other results, we find in the latter case a divergent behavior of the inhomogeneous universal scaling functions associated with the surface specific heat, generated by the interface between the wall and the bulk phase of a macroscopically thick wetting film. We show that the singularity of this profile near the interface in spatial dimension three is governed by a power-law divergence with the exponent 2α/β, while it is of logarithmic nature in the mean-field limit. It turns out that this feature has a strong influence on the values of the universal surface amplitudes, regarding both their magnitude and sign.

Keywords: Surface critical phenomena; Adsorption; Ising model (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:594:y:2022:i:c:s0378437121009213

DOI: 10.1016/j.physa.2021.126701

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