Monte Carlo critical isotherms for Ising lattices

Abstract

Monte Carlo investigations of magnetization versus field, $M_c(H)$, at the critical temperature provide direct accurate results on the critical exponent ${\delta }^{-1}$ for one, two, three and four-dimensional lattices: ${\delta }_{1D}^{-1}$=0, ${\delta }_{2D}^{-1}$=0.0666(2)$\simeq$1/15, ${\delta }_{3D}^{-1}$=0.1997(4)$\simeq$1/5, ${\delta }_{4D}^{-1}$=0.332(5)$\simeq$1/3. This type of Monte Carlo data on $\delta$, which is not easily found in studies of Ising lattices in the current literature, as far as we know, defines extremely well the numerical value of this exponent within very stringent limits.

arXiv comment5 pages, 4 figures. Sent to Europhysics Letters

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• Generalized susceptibilities of net-baryon number based on the 3-dimensional Ising universality class
• Cumulants in the 3-dimensional Ising, O(2) and O(4) spin models
• Fixed point behavior of cumulants in the three-dimensional Ising universality class