Monte Carlo study of a generalized icosahedral model on the simple cubic lattice

Martin Hasenbusch

Published 2020-05-09Version 1

We study the critical behavior of a generalized icosahedral model on the simple cubic lattice. In addition to twelve vectors of unit length which are given by the normalized vertices of the icosahedron, the field variable is allowed to take the value $(0,0,0)$. There is a parameter $D$ that controls the density of zeros. For a certain range of $D$, the model undergoes a second order phase transition. On the critical line, $O(3)$ symmetry emerges. Furthermore, we demonstrate that within this range, there is a value, where leading corrections to scaling vanish. We perform Monte Carlo simulations for lattices of a linear size up to $L=400$ by using a hybrid of local Metropolis and cluster updates. The motivation to study this particular model is mainly of technical nature. Less memory and CPU time are needed than for a model with $O(3)$ symmetry at the microscopic level. As the result of a finite size scaling analysis we obtain $\nu=0.71164(10)$, $\eta=0.03784(5)$ and $\omega=0.759(2)$ for the critical exponents of the three-dimensional Heisenberg universality class. The estimate of the irrelevant RG-eigenvalue that is related with the breaking the $O(3)$ symmetry is $y_{ico}=-2.19(2)$.