Scaling Properties of Hadron Production in the Ising Model for Quark-Hadron Phase Transition

Earlier study of quark-hadron phase transition in the Ginzberg-Landau theory is reexamined in the Ising model, so that spatial fluctuations during the transition can be taken into account. Although the dimension of the physical system is 2, as will be argued, both d=2 and d=4 Ising systems are studied, the latter being theoretically closer to the Ginzberg-Landau theory. The normalized factorial moments F_q are used to quantify multiplicity fluctuations, and the scaling exponent \nu is used to characterize the scaling properties. It is found by simulation on the Ising lattice that \nu becomes a function of the temperature T near T_c. The average value of \nu over a range of T<T_c agrees with the value of 1.3 derived analytically from the Ginzberg-Landau theory. Thus the implications of the mean-field theory are not invalidated by either the introduction of spatial fluctuations or the restriction to a 2D system.