Extrapolated Renormalization Group Calculation of the Surface Tension in Square-Lattice Ising Model.

摘要

By using self-dual clusters (whose sizes are characterized by the numbers b=2, 3, 4, 5) within a real space renormalization group framework, the longitudinal surface tension of the square-lattice first-neighbour 1/2-spin ferromagnetic Ising model is calculated. The exact critical temperature T sub(c) is recovered for any value of b; the exact assymptotic behaviour of the surface tension in the limit of low temperatures is analytically recovered; the approximate correlation length critical exponents monotonically tend towards the exact value nu =1 (which, at two dimensions, coincides with the surface tension critical exponent mu ) for increasingly large cells; the same behaviour is remarked in what concerns the approximate values for the surface tension amplitude in the limit T implies T sub(c). Four different numerical procedures are developed for extrapolating to b implies infinite the renormalization group results for the surface tension, and quite satisfactory agreement is obtained with Onsager's exact expression (error varying from zero to a few percent on the whole temperature domain). Furthermore the set of RG surface tensions is compared with a set of biased surface tensions (associated to appropriate misfit seams), and find only fortuitous coincidence among them. (Atomindex citation 12:620084)