Abstract
We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary n-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region.
Highlights
The two-dimensional case holds a central role because of the availability of nonperturbative techniques which lead to exact solvability of the strongly fluctuating regime
We show how the field-theoretic formalism [30] can be extended to the calculation of n-point correlation functions for arbitrary n
We will illustrate firstly the case of correlations of the order parameter field, for which we will single out those contributions which are originated by interfacial fluctuations from those which are genuinely due to bulk fluctuations
Summary
We illustrate the calculation of the n-point correlation function of the spin field on the finite strip showed in figure 1. The large-distance decay of the spin-spin correlation function is completely characterized by the state with the lowest number of particles. It is not necessary, let us take the example of the thermally deformed Ising field theory (the bulk magnetic field is identically zero). For the multi-kink state the low-rapidity behavior shows that the corresponding Un-function is proportional to e−mRe−(N −1)m(yj −yj−1). The single-kink contribution to the correlation function given by (2.15) is exact up to exponentially small corrections in the vertical separation of adjacent spin fields. On we will focus on the single-kink term which dominates the asymptotic behavior of correlation functions in the limit of interest specified by the strong inequalities in (2.10). The disconnected parts of the correlation function will be investigated in section 2.3 and the full result for Gn will be supplied section 2.4
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