SURFACE-TENSION OF THE INDUCED MAGNETIZATION IN THE 1D ISOTROPIC XY-MODEL

The surface tension of the induced magnetization in the one-dimensiona l 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 functio n technique. At T = 0 the system undergoes a quantum transition in the bulk driven by the field which is associated to the induced renormali zed magnetization. In this temperature limit, the surface tension is d etermined, and it is shown that, when properly renormalized, it follow s a scaling law near the critical point, with a critical exponent mu e qual to 1. A brief review is presented for the calculations of the cri tical exponents and it is also shown that they satisfy the known relat ions, 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 re sult, the dimension d in the relation mu = (d - 1)nu for classical sys tems should be replaced by the effective dimension d + z for quantum t ransitions.