Conformal invariance and finite size effects in critical two dimensional statistical models

Francisco Castilho Alcaraz

This paper is concerned with the critical properties of a family of self-dual two-dimensional Z(N) models whose bulk free energy is exactly known at the self-dual point. The author's analysis is performed by studying the finite-size behaviour of the corresponding one-dimensional quantum Hamiltonians which also possess an exact solution at their self-dual point. By exploring finite-size scaling ideas and the conformal invariance of the critical infinite system the author calculates, for N up to 8, the critical temperature and critical exponents as well as the central charge associated with the underlying conformal algebra. The results strongly suggest that the Z(N) quantum field theory of Zamolodchikov and Fateev is the underlying field theory associated with these statistical mechanical systems. The author also tests for the Z(5) case, the conjecture that these models correspond to the bifurcation points in the phase diagram of the General Z(N) spin model, where a massless phase originates.

Daniel Harry Friedan, Zongan Qiu, Stephen H. Shenker

John Cardy

Peter H. Kleban, Reinhard Hentschke

Using the consequences of conformal invariance we examine the effects of finite size and boundary conditions on the scattering line shape for two-dimensional systems at bulk critical points. The "apparent exponent" behavior observed for free boundary conditions is modeled analytically, and the influence of the finite geometry on the overall line shape is discussed. For fixed boundary conditions critical effects are strongly suppressed.

Henk W. J. Blöte, John Cardy, M. P. Nightingale

We show that for conformally invariant two-dimensional systems, the amplitude of the finite-size corrections to the free energy of an infinitely long strip of width L at criticality is linearly related to the conformal anomaly number c, for various boundary conditions. The result is confirmed by renormalization-group arguments and numerical calculations. It is also related to the magnitude of the Casimir effect in an interacting one-dimensional field theory, and to the low-temperature specific heat in quantum chains.

Malte Henkel