Logarithmic Corrections in the 2D XY Model TeX Export

@article{citeulike:5120204, abstract = {Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square \$L \times L\$ lattices, the scaling behavior of the susceptibility \$\chi\$ and correlation length \$\xi\$ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections \$(ln L)^{-2r}\$ in the finite-size scaling region and \$(ln \xi)^{-2r}\$ in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to \$512^2\$ we obtain \$r = -0.0270(10)\$, in agreement with recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to \$\xi \approx 140\$ in the high-temperature phase, however, we arrive at quite a different estimate of \$r = 0.0560(17)\$, which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation.}, archivePrefix = {arXiv}, author = {Janke, Wolfhard}, citeulike-article-id = {5120204}, citeulike-linkout-0 = {http://arxiv.org/abs/hep-lat/9609045}, citeulike-linkout-1 = {http://arxiv.org/pdf/hep-lat/9609045}, eprint = {hep-lat/9609045}, keywords = {xy-model}, month = {Sep}, posted-at = {2009-07-11 20:35:49}, priority = {2}, title = {Logarithmic Corrections in the 2D XY Model}, url = {http://arxiv.org/abs/hep-lat/9609045}, year = {1996} }

TY - JOUR ID - citeulike:5120204 L3 - citeulike-article-id:5120204 N2 - Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square $L \times L$ lattices, the scaling behavior of the susceptibility $\chi$ and correlation length $\xi$ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections $(ln L)^{-2r}$ in the finite-size scaling region and $(ln \xi)^{-2r}$ in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to $512^2$ we obtain $r = -0.0270(10)$, in agreement with recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to $\xi \approx 140$ in the high-temperature phase, however, we arrive at quite a different estimate of $r = 0.0560(17)$, which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation. TI - Logarithmic Corrections in the 2D XY Model KW - xy-model AU - Janke, Wolfhard PY - 1996/Sep/28/ UR - http://arxiv.org/abs/hep-lat/9609045 ER -