Investigation of the Disordered Antiferromagnetic Ising Model with the Effects of Random Magnetic Fields

Computer simulation of phase transitions is made by the Monte Carlo method using a three-dimensional disordered antiferromagnetic Ising model in the external magnetic field. It is found that in the case where the spin concentration in a system is lower than a threshold one, the effects of random magnetic fields destroy the second-order phase transition and lead to the first-order phase transition into a new phase state of the system characterized by a ground spin-glassy state and metastable energy states at finite temperatures. The dependence of the threshold concentration on the external magnetic field is revealed.     

Changes in quantum states of atoms in a markovian thermostat

We solve the nonlinear Schrödinger equation, taking into account self-interaction through the surrounding medium. We have found that such atoms have a countable set of stable equilibrium states, coinciding with the wave eigenfunctions of an individual atom. We show that transitions of an atom from equilibrium quantum states corresponding to less excited levels to more excited levels occur in jumps, while transitions from equilibrium states corresponding to upper levels to lower levels may occur either as radiationless transitions or be accompanied by spontaneous emission at the eigenfrequency of the quantum transition. We have found the conditions for which a change in the topological structure of the atomic wavefunction is possible.     

Density criteria for a family of measures in a certain space of two-parameter Lipschitz functions

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 4, pp. 27–32, July–August, 1990.     

Proof of existence theorems for the two-parameter martingale problem

Translated from Sibirskii Matemaiicheskii, Vol. 36, No. 2, pp. 248–265, March–April, 1995.     

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.     

Phase transitions and peculiarities of the growth of nuclei of the new phase of a substance

We describe phase transitions using a one-dimensional fractional differential kinetic equation of the Fokker-Planck type. We find a general solution describing the growth of nuclei during phase transitions in a fractal medium.