Abstract
The spin- 3 2 Ising model on the square lattice with nearest-neighbor ferromagnetic exchange interactions (both bilinear ( J) and biquadratic ( K)) and crystal-field interaction (Δ) is studied using a renormalization-group transformation in position-space based on the Migdal-Kadanoff recursion relations. The global phase diagram in ( J, K, Δ) space (with J, K ⩾ 0) is found to have two surfaces of critical phase transitions and two surfaces of first-order phase transitions. These surfaces are variously bounded by an ordinary trictical line, an isolated critical line of end points, and a line of multicritical points. The global connectivity and local exponents of the thirteen separate fixed points underlying this quite complicated structure are determined.
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