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Phase transitions in a classical Heisenberg spin model of a chiral helimagnetwith the Dzyaloshinskii--Moriya (DM) interaction in three dimensions arenumerically studied. By using the event-chain Monte Carlo algorithm recentlydeveloped for particle and continuous spin systems, we perform equilibriumMonte Carlo simulations for large systems up to about $10^6$ spins. Withoutmagnetic fields, the system undergoes a continuous phase transition withcritical exponents of the three-dimensional \textit{XY} model, and a uniaxialperiodic helical structure emerges in the low temperature region. In thepresence of a magnetic field perpendicular to the axis of the helicalstructure, it is found that there exists a critical point on the temperatureand magnetic-field phase diagram and that above the critical point the systemexhibits a phase transition with strong divergence of the specific heat and theuniform magnetic susceptibility.

Phase transitions and ordering structures of a model of chiral helimagnet in three dimensions