Energy fluctuations and the singularity of specific heat in 3D Ising model

We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat C-V based on the finite-size scaling of its maximal values C-V(max) depending on the linear size of the lattice L. An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of C-V. The simulations made up to L less than or equal to 128 with application of the Wolff's cluster algorithm allowed us to verify the possible power-like as well as logarithmic singularity of the specific heat predicted by different theoretical treatments. The most challenging and interesting result we have obtained is that the finite-size scaling of C-V(max) in 3D Ising model is well described by a logarithmic rather than power-like ansatz, just like in 2D case. Another modification of our iterative method has been considered to estimate the critical coupling of 3D Ising model from the Binder cumulant data within L is an element of [96; 384]. Furthermore, the critical exponent beta has been evaluated from the simulated magnetization data within the range of reduced temperatures t greater than or equal to 0.000086 and system sizes L less than or equal to 410.