Monte Carlo simulations of the SU(2) lattice gauge theory with SIN action and EXP action are performed by using the icosahetral subgroup. We obtain that the first order phase transition points due to the nature of discrete subgroup are βc′≈9.2±0.2 and βc′= 6.8±0.2 respectively. The plaquette energy and specific heat of present case are in good agreement with that of the SU(2) group. Therefor, we verify that for two kinds of actions mentioned above, using discrete subgroup instead of SU(2) group is reasonable and provides the foundation for further calculations by means of the icosahetral subgroup.
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