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DY: Fachverband Dynamik und Statistische Physik

DY 7: Critical Phenomena and Phase Transitions

DY 7.4: Talk

Monday, March 18, 2024, 12:30–12:45, BH-N 128

Cubic fixed point in three dimensions: Monte Carlo simulations of the φ⁴ model on the simple cubic lattice — •Martin Hasenbusch — Universität Heidelberg, Heidelberg, Deutschland

We study the cubic fixed point for N=3 and 4 by using finite-size scaling applied to data obtained from Monte Carlo simulations of the N-component φ⁴ model on the simple cubic lattice. We generalize the idea of improved models to a two-parameter family of models. The two-parameter space is scanned for the point, where the amplitudes of the two leading corrections to scaling vanish. To this end, a dimensionless quantity is introduced that monitors the breaking of the O(N) invariance. For N=4, we determine the correction exponents ω₁=0.763(24) and ω₂=0.082(5). In the case of N=3, we obtain Y₄=0.0142(6) for the renormalization group exponent of the cubic perturbation at the O(3)-invariant fixed point, while the correction exponent ω₂=0.0133(8) at the cubic fixed point. Simulations close to the improved point result in the estimates ν=0.7202(7) and η=0.0371(2) of the critical exponents of the cubic fixed point for N=4. For N=3, at the cubic fixed point, the O(3) symmetry is only mildly broken and the critical exponents differ only by little from those of the O(3)-invariant fixed point. We find −0.00001 ≤ η_cubic−η_O(3) ≤ 0.00007 and ν_cubic−ν_O(3)=−0.00061(10).

Keywords: Monte Carlo; Lattice; cubic symmetry