A new spin glass model defined on the N×N 2-dimensional random lattice with the SO (3) spin variables is proposed, and. studied by Monte Carlo simulations. The thermodanamics, such as the internal energy and specific heat per spin and the topological excition are calculated. The thermal hysteresis and mix-phase runs are also made to obtain some information of the Phase transitions. A higher-order, instead of the usual first-or second-order, Phase transition due to the vortex condensation is found. Moreover, the results show the important frustration and disorder effects which are main causes of low-temperature properties of sPin glass.

Using Monte Carlo techniques we study the SU(2) lattice gauge theory with Sin 1-Sin(T_rU_p/2) action at finite temperatures.A deconfinement transition at high temperature is observed. The critical point is T_c=334±40Mev, which is consistent with that obtained by using Wilson's action and others.

A fast sampling method which can afford saving much computer time was suggested.We studied the behaviour of this method near the critical points for Z₂ and SU(3) gauge groups.It is found that this method will lose his effect when passes through the first order phase transition points.This character will be used to find the first order transition according to some program.