On the Numerical Calculation of Frustrations in the Ising Model

A quantitative measure of magnetic frustration is defined as a thermodynamically averaged relative number of excited pair interactions in the Hamiltonian of a system. The Metropolis algorithm has been upgraded to a hybrid multispin Monte Carlo method using a quasi-Markov chain of random events. The combination of canonical and multicanonical sampling of the Gibbs distribution in one computational scheme has made it possible to determine the temperature dependences of the increment in the number of excitations and the entropy increment of the hexagonal lattice of artificial spin ice and to calculate the configuration of the ground state. The temperature behavior of the frustration parameter of a geometrically frustrated hexagonal lattice of point dipoles is obtained numerically using the developed method. This method for calculating the quantitative measure of frustrations can be used to process experimental data.