Regensburg 2022 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 26: Critical Phenomena and Phase Transitions

DY 26.1: Vortrag

Mittwoch, 7. September 2022, 10:00–10:15, H20

Percolation properties of the Ising spin glass in two dimensions — •Lambert Münster and Martin Weigel — Institut für Physik, TU Chemnitz, 09107 Chemnitz, Germany

Cluster representations provide a framework to study critical phenomena from the geometrical perspective of percolation. Due to frustration the common Fortuin-Kasteleyn cluster representation of ferromagnets is not well suited to describe the spin-glass transition [1,2]. The order parameter of this transition is the overlap which is naturally defined with respect to two replicas. In the present work we hence study a two-replica cluster representation [3] of the two-dimensional Ising spin glass by performing Monte Carlo simulations at low temperatures. Our data is consistent with the existence of a zero-temperature percolation transition in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is proportional to the difference in density of the two largest clusters.
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[2] H. Fajen, A. K. Hartmann, and A. P. Young, Phys. Rev. E 102, 012131, (2020).
[3] J. Machta, C. M. Newman, and D. L. Stein, J. Stat. Phys. 130, 113, (2008).