Renormalization and scaling of a two-dimensional Ising system in a transverse field at Tc>0

A.L. Stella and F. Toigo

Physica A: Statistical Mechanics and its Applications, 1977, vol. 89, issue 1, 175-190

Abstract: A quantum generalization of the Niemeijer and van Leeuwen (N-vL) renormalization group transformation is constructed which allows to study the critical properties (at Tc>0) of a two-dimensional Ising system with a transverse field on a triangular lattice. Explicit calculations are performed in a second order cumulant expansion. Only one fixed point is found corresponding to the same Ising-like hamiltonian given by N-vl. The linearized transformation has a zero eigenvalue associated with Γ, the transverse field strength. The critical properties of the system are briefly discussed; in particular we show that the singular behaviour of the transverse susceptibility at Γ = 0, which turns out to be of the same kind as that of the energy density, is explained by the existence of such a zero eigenvalue. Our arguments suggest a natural extension of this result to three dimensions.

Date: 1977
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:89:y:1977:i:1:p:175-190

DOI: 10.1016/0378-4371(77)90148-0

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