Monte Carlo study of a generalized icosahedral model on the simple cubic lattice Article Swipe
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· 2020
· Open Access
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· DOI: https://doi.org/10.1103/physrevb.102.024406
· OA: W3023029041
We study the critical behavior of a generalized icosahedral model on the\nsimple cubic lattice. The field variable of the icosahedral model might take\none of twelve vectors of unit length, which are given by the normalized\nvertices of the icosahedron, as value. Similar to the Blume-Capel model, where\nin addition to $-1$ and $1$, as in the Ising model, the spin might take the\nvalue $0$, we add in the generalized model $(0,0,0)$ as allowed value. There is\na parameter $D$ that controls the density of these voids. For a certain range\nof $D$, the model undergoes a second-order phase transition. On the critical\nline, $O(3)$ symmetry emerges. Furthermore, we demonstrate that within this\nrange, similar to the Blume-Capel model on the simple cubic lattice, there is a\nvalue of $D$, where leading corrections to scaling vanish. We perform Monte\nCarlo simulations for lattices of a linear size up to $L=400$ by using a hybrid\nof local Metropolis and cluster updates. The motivation to study this\nparticular model is mainly of technical nature. Less memory and CPU time are\nneeded than for a model with $O(3)$ symmetry at the microscopic level. As the\nresult of a finite-size scaling analysis we obtain $\\nu=0.71164(10)$,\n$\\eta=0.03784(5)$, and $\\omega=0.759(2)$ for the critical exponents of the\nthree-dimensional Heisenberg universality class. The estimate of the irrelevant\nrenormalization group eigenvalue that is related with the breaking the $O(3)$\nsymmetry is $y_{ico}=-2.19(2)$.\n
