Domain magnetization approach to the isothermal critical exponent

We propose a method for calculating the isothermal critical exponent $δ$ in Ising systems undergoing a second-order phase transition. It is based on the calculation of the mean magnetization time series within a small connected domain of a lattice after equilibrium is reached. At the pseudocritical point, the magnetization time series attains intermittent characteristics and the probability density for consecutive values of mean magnetization within a region around zero becomes a power law. Typically the size of this region is of the order of the standard deviation of the magnetization. The emerging power-law exponent is directly related to the isothermal critical exponent $δ$ through a simple analytical expression. We employ this method to calculate with remarkable accuracy the exponent $δ$ for the square-lattice Ising model where traditional approaches, like the constrained effective potential, typically fail to provide accurate results.

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