ANALYTIC AND NUMERICAL STUDY OF A HIERARCHICAL SPIN MODEL
Authors: Yu.Kozitsky (Institute of Mathematics of Marie Curie-Sklodowska University, 20--031 Lublin, Poland; Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 290011 Lviv, Ukraine), M.Kozlovskii, T.Krokhmalskii (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 290011 Lviv, Ukraine)
A simple hierarchical scalar spin model is studied analytically and numerically in the vicinity of its critical point. The dependence of the finite size (i.e. calculated for a large but finite number of spins) susceptibility and the location of zeros of the model partition function on the number of spins at the critical point is described analytically. It is also shown analytically that the finite size correlation length in such a model diverges at the critical point slower than it is supposed in the finite size scaling theory. Certain numerical information about the critical point and ordered phase is given. In particular, the critical temperature of the model and the critical index describing the order parameter are calculated for various values of the interaction parameter.
Comments: Figs. 8, Refs. 22, Tabs. 0.
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