The critical Ising model on a torus with a defect line

Abstract

The critical Ising model in two dimensions with a specific defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically the partition function and the asymptotic expansions of the free energy and inverse correlation lengths for an infinitely long cylinder of circumference Lx. We find that finite-size corrections to scaling are of the form ak/Lx2k1a_k/L^{2k-1}_x for the free energy f and bk(p)/Lx2k1b_k(p)/L_x^{2k-1} and ck(p)/Lx2k1c_k(p)/L_x^{2k-1} for inverse correlation lengths ξp1\xi^{-1}_p and ξLp1\xi^{-1}_{L-p} , respectively, with integer values of k. By exact evaluation we find that the amplitude ratios bk(p)/akb_k(p)/a_k and ck(p)/akc_k(p)/a_k are universal and verify this universal behavior using a perturbative conformal approach

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EDP Sciences OAI-PMH repository (1.2.0)

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Last time updated on 10/04/2020

This paper was published in EDP Sciences OAI-PMH repository (1.2.0).

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