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Based on Novotny's transfer-matrix method, we simulated the (stacked)triangular Ising antiferromagnet embedded in the space with the dimensionsvariable in the range 2 \le d \le 3. Our aim is to investigate the criticalityof the XY universality class for 2 \le d \le 3. For that purpose, we employedan 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 toN=17, we calculated the $d$-dependent correlation-length critical exponent\nu(d). Our simulation result \nu(d) appears to interpolate smoothly the knowntwo limiting cases, namely, the KT and d=3 XY universality classes, and theintermediate behavior bears close resemblance to that of the analytical formulavia the 1/N-expansion technique. Methodological details including themodifications specific to the present model are reported

physical review. e, statistical, nonlinear and soft matter physics

Finite-size-scaling analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>universality class between two and three dimensions: An application of Novotny’s transfer-matrix method

Finite-size-scaling analysis of theXYuniversality class between two and three dimensions: An application of Novotny’s transfer-matrix method