6533b7dafe1ef96bd126f525

RESEARCH PRODUCT

Finite-size scaling analysis of the ?4 field theory on the square lattice

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Monte-Carlo calculations are performed for the model Hamiltonian ℋ = ∑i[(r/2)Φ 2(i)+(u/4)/gF4(i)]+∑ (C/2)[Φ (i)−Φ(j)]2 for various values of the parametersr, u, C in the crossover region from the Ising limit (r→-∞,u+∞) to the displacive limit (r=0). The variableφ(i) is a scalar continuous spin variable which can lie in the range-∞<φ(i)<+∞, for each lattice site (i).φ(i) is a priori selected proportional to the single-site probability in our Monte Carlo algorithm. The critical line is obtained in very good agreement with other previous approaches. A decrease of apparent critical exponents, deduced from a finite-size scaling analysis, is attributed to a crossover toward mean-field values at the displacive limit. The relation of this model to the coarse-grained Landau-Ginzburg-Wilson free-energy functional of Ising models is discussed in detail, and, by matching local moments 〈Φ 2(i)〉, 〈Φ 4(i)〉 to corresponding averages of subsystem blocks of Ising systems with linear dimensionsl=5 tol=15, an explicit construction of this coarse-grained free energy is attempted; self-consistency checks applied to this matching procedure show qualitatively reasonable behavior, but quantitative difficulties remain, indicating that higher-order terms are needed for a quantitatively satisfactory description.