Universality in the critical exponents δ and η

V. A. Rabinovich, Yu. E. Sheludyak

Masuo Suzuki

The extended scaled equation of state (namely, the scaled form of the wave-number dependent nonlinear susceptibility) is confirmed up to the first order of 1/n, in the classical n-vector model with general range of interactions. Critical exponents γ, δ, η, ν and Δ are evaluated systematically to order 1/n, both for short-range and long-range interactions to check universality and scaling relations.

Masuo Suzuki

A general formulation for the expansion of the partition function in inverse powers of spin dimensionality n is given in the classical n-vector model in the presence of an inhomogeneous magnetic field. The critical exponents δ and η have been evaluated through the first order of 1/n, as functions of dimensionality d and potential-range σ. The universality and scaling relations on the critical exponents have been partially verified.

J. C. Le Guillou, Jean Zinn‐Justin

Roman Krčmár, Ladislav Šamaj

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents η_{e} and δ_{e} which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.