Abstract
We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge, we show how the problem can be studied analytically from first principles, starting from the degrees of freedom (particle modes) of the bulk field theory. After deriving the passage probability of the interface and the order parameter profile in the regime in which the interface is not bound to the wall, we show how the theory accounts at the fundamental level also for the binding transition and its key parameter.
Highlights
An important problem in the theory of statistical systems close to criticality is that of providing a fundamental treatment of phenomena involving different length scales
Working slightly below the critical temperature, where universal properties emerge, we show how the problem can be studied analytically from first principles, starting from the degrees of freedom of the bulk field theory
The divergence of the correlation length ξ as the critical temperature Tc is approched is at the origin of universality, namely the existence of quantities such as critical exponents whose values only depend on global properties
Summary
An important problem in the theory of statistical systems close to criticality is that of providing a fundamental treatment of phenomena involving different length scales. It is far from obvious how to derive analytical results that simultaneously encode scaling and interfacial properties, which are related to short and large distance effects, respectively It has been recently shown [3] how the problem can be dealt with within the particle description of field theory. The bulk field theory possesses a complete basis of particle states that allow to write the configurational sums in momentum space, and this in the case of boundary conditions that induce the presence of an interface. We show how the problem of the interface in presence of the wall is implemented starting from the particle modes of the bulk field theory.
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