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≤d≤≤3. Our aim is to investigate the criticality of the XY universality class for 2≤d≤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≤d≤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 Kosterlitz-Thouless (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.
|Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|Published - Apr 2005
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics