Surface Tension of the Induced Magnetization in the 1D Isotropic XY-Model

Abstract

The surface tension of the induced magnetization in the one-dimensional isotropic ferromagnetic XY-model (s = 1/2, open chain) is considered. The magnetization domains are induced by an inhomogeneous transverse field, and the model can be exactly solved by using the Green function technique. At T = 0 the system undergoes a quantum transition in the bulk driven by the field which is associated to the induced renormalized magnetization. In this temperature limit, the surface tension is determined, and it is shown that, when properly renormalized, it follows a scaling law near the critical point, with a critical exponent μ equal to 1. A brief review is presented for the calculations of the critical exponents and it is also shown that they satisfy the known relations, provided the effective classical dimension is equal to 3. Since the dynamic exponent z is equal to 2, this result confirms the dynamic shift in the dimensionality of the system, d+z, as expected for the quantum transitions. It is also shown that, consistently with this result, the dimension d in the relation μ = (d-1)ν for classical systems should be replaced by the effective dimension d+z for quantum transitions.