Article

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

10/2001; 34(42):8733-8750. DOI: 10.1088/0305-4470/34/42/302
Source: arXiv

ABSTRACT

We investigate the presence of irrelevant operators in the two-dimensional Ising model perturbed by a magnetic field, by studying the corrections induced by these operators in the spin-spin correlator of the model. To this end we perform a set of high-precision simulations for the correlator both along the axes and along the diagonal of the lattice. By comparing the numerical results with the predictions of a perturbative expansion around the critical point we find unambiguous evidence of the presence of such irrelevant operators. It turns out that among the irrelevant operators the one which gives the largest correction is the spin-4 operator T 2 + bar T2, which accounts for the breaking of the rotational invariance due to the lattice. This result agrees with what was already known for the correlator evaluated exactly at the critical point and also with recent results obtained in the case of the thermal perturbation of the model.

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Available from: Michele Caselle
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• "Moreover, in the nearest-neighbor spin-1/2 two-dimensional Ising model, it was further assumed for many years that there are no irrelevant operators [12] [13]; indeed this assumption was confirmed numerically through order (T − T c ) 3 at least as regards the bulk behavior of the susceptibility in the isotropic square-lattice Ising model [13]. However, several authors have recently found overwhelming evidence that there are indeed irrelevant operators playing a role in the two-dimensional Ising model [14] [15] [16] [17] [18] [19] [20]. In particular, for the square-lattice Ising model they have found by studying the bulk magnetic susceptibility that there is one irrelevant operator contributing to order (T − T c ) 4 and there is (at least) one irrelevant operator contributing to order (T − T c ) 6 . "
Article: Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus. II. Triangular and hexagonal lattices
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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.
Preview · Article · Nov 2001 · Journal of Physics A General Physics
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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.
Preview · Article · Oct 2000 · Journal of Physics A General Physics
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Article: Irrelevant operators in the two-dimensional Ising model
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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.
Full-text · Article · Jul 2001 · Journal of Physics A General Physics