Finite-size-scaling analysis of the XY universality class between two and three dimensions: An application of Novotny's transfer-matrix method

Abstract

Based on Novotny's transfer-matrix method, we simulated the (stacked) triangular Ising antiferromagnet embedded in the space with the dimensions variable in the range 2 \le d \le 3. Our aim is to investigate the criticality of the XY universality class for 2 \le d \le 3. For that purpose, we employed an extended version of the finite-size-scaling analysis developed by Novotny, who utilized this scheme to survey the Ising criticality (ferromagnet) for 1 \le d \le 3. Diagonalizing the transfer matrix for the system sizes N up to N=17, we calculated the $d$-dependent correlation-length critical exponent ν(d). Our simulation result ν(d) appears to interpolate smoothly the known two limiting cases, namely, the KT and d=3 XY universality classes, and the intermediate behavior bears close resemblance to that of the analytical formula via the 1/N-expansion technique. Methodological details including the modifications specific to the present model are reported.

References in corpus (3)

• The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
• Multi-criticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny's transfer-matrix formalism
• Tensor Product State Formulation for the Spin 1/2 Antiferromagnetic XXZ Model on the Checkerboard Lattice

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• Unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating scalar field theories at all loop orders
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