# Correction induced by irrelevant operators in the correlators of the two-dimensional Ising model in a magnetic field

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Michele Caselle, Jun 29, 2015 Available from:- [Show abstract] [Hide abstract]

**ABSTRACT:**We compute the finite-size corrections to the free energy, internal energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a triangular and hexagonal lattices wrapped on a torus. We find the general form of the finite-size corrections to these quantities, as well as explicit formulas for the first coefficients of each expansion. We analyze the implications of these findings on the renormalization-group description of the model.Journal of Physics A General Physics 11/2001; DOI:10.1088/0305-4470/35/8/304 -
##### Article: Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus

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**ABSTRACT:**We analyze the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L^{-3} to the energy and the corrections of order L^{-2} and L^{-3} to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: only integer powers of L^{-1} occur, unmodified by logarithms (except of course for the leading $\log L$ term in the specific heat); and the energy expansion contains only odd powers of L^{-1}. In the specific-heat expansion any power of L^{-1} can appear, but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion.Journal of Physics A General Physics 10/2000; 34(7). DOI:10.1088/0305-4470/34/7/307 - [Show abstract] [Hide abstract]

**ABSTRACT:**By using conformal-field theory, we classify the possible irrelevant operators for the Ising model on the square and triangular lattices. We analyze the existing results for the free energy and its derivatives and for the correlation length, showing that they are in agreement with the conformal-field theory predictions. Moreover, these results imply that the nonlinear scaling field of the energy-momentum tensor vanishes at the critical point. Several other peculiar cancellations are explained in terms of a number of general conjectures. We show that all existing results on the square and triangular lattice are consistent with the assumption that only nonzero spin operators are present.Journal of Physics A General Physics 07/2001; DOI:10.1088/0305-4470/35/23/305