A connection between integrable Z(N) models and off-critical non-unitary theories

H. Babujian, Angela Foerster, Michael Karowski

春彦 松尾

Leon A. Takhtajan

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.

Francisco Castilho Alcaraz

Considers the critical behaviour of a particular set of onedimensional self-dual models with Z(N) symmetry (N <or= 5). The critical indices are evaluated using standard finite-size scaling and by exploiting their relations with the mass gap amplitudes predicted by conformal invariance. The results strongly suggest that the recently introduced Z(N) quantum field theory is the underlying field theory for these statistical mechanics models.

Gesualdo Delfino A, Giuseppe Mussardo, P. Simonetti