Regensburg 2022 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 26: Critical Phenomena and Phase Transitions

DY 26.2: Vortrag

Mittwoch, 7. September 2022, 10:15–10:30, H20

Replica-symmetry breaking for directed polymers in correlated random media — •Alexander K. Hartmann — Institute of Physics, University of Oldenburg

The phase-space behavior of complex system can often be described by replica-symmetry breaking (RSB), as introduced by Giorgio Parisi for mean-field Ising spin glasses [1] and highlighted by the Nobel price 2021. Numerically, spin glasses and related problems are notoriously hard to study, such that models exhibiting RSB have been treated so far only for small sizes. Here, directed polymers on 1+1 dimensional lattices at temperature T are considered [2]. New ensembles with correlations of the disorder as well as fractal patterning are introduced [3]. This model allows for direct sampling in perfect thermal equilibrium for large system sizes of N=L²= 32768 × 32768 ≈ 10⁹ sites. Fluctuations of the free energy and transverse extension are obtained and compared with the standard uncorrelated ensemble. The phase-space structure is studied via the distribution of overlaps, hierarchical clustering methods and analysis of ultrametricity. One ensemble shows a simple behavior like a ferromagnet. The other two ensembles exhibit indications for multiple RSB. In total, the present model ensembles offer convenient numerical access to comprehensively studying complex RSB-like behavior.

[1] G. Parisi, Phys. Rev. Lett. 43, 1754 (1979)

[2] A. K. Hartmann, Big Practical Guide to Computer Simulations, World-Scientific, Singapore (2015)

[3] A. K. Hartmann, Euro. Phys. Lett. 137, 41002 (2022)