Critical Behaviour of Some 2D Lattice Models

G. Kamieniarzb, H.W.J. Blötea and R. Dekeyserb aFaculty of Applied Physics, Delft University of Technology, The Netherlands bInstitute of Theoretical Physics, KU Leuven, Belgium

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The density series of the non-interacting hard-square lattice gas model are reanalyzed by the ratio, Dlog Padé and differential approximant methods. The problem of poor consistency between series and other results is resolved. Transfer matrix calculations are performed, implementing both finite-size scaling and conformal invariance. Very accurate estimates of the critical exponents yt, and yh are obtained in agreement with Ising universality. Furthermore, an improvement of the value of the critical density ρc is found. In addition, the universal critical-point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic Ising models on the square and on the triangular lattice with periodic boundary conditions are reported.

DOI: 10.12693/APhysPolA.85.389 PACS numbers: 05.50.+q, 64.60.-i, 64.60.Cn, 64.60.Ak, 64.60.Fr, 75.40.Mg