The Monte Carlo simulational study of the Ising model is explained. The Ising model is the most elementary subject in the statistical physics, and its simulational study is a typical computing science. Many new problems of the computing science have been appearing firstly in this Ising problems because the most intensive simulation and the most extensive study have made for them. Some recent remarkable results in the simulational methods come from the Ising Monte Carlo, in which many computing researchers studying other problems will be interested, are introduced. The statistical-dependence analysis provides a new and a very practical method to study the correlation in a temporal data. The recycle method gives an efficient way to generate and use the random number.

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A statistical mechanical placements theory for gate array LSI and its applications for interconnection length prediction and wireablity analysis are described. A gate array is defined as v_1×v_2 grid graph and logic circuit is done as a graph with at most one edge between a pair of verteices. In a placement we condider a wire as a particle and a wire length as a particle energy level in statistical mechanics. Then distribution of wire length k is expressed by E_k^0=W_k/(1+exp(-v+kup)(k=l, 2, …) same as FermiDirac Statistics. The approximated distribution is describe by P_k=ke^<-(k-1)/T>(1-e^<-1/T>)^2 with temperature T and then the mean R is (l+e^<-1/T>)/(1-e^<-1/T>). This theoritical distribution fits to actual wire length distribution in spite of unique parameter R(or T). A statistical optimal placement equation is deduced for the minimum average wire length. Solutions of the equation are applicable to wire length prediction and wireability analysis practically.

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