Regensburg 2025 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 6: Critical Phenomena and Phase Transitions
DY 6.2: Talk
Monday, March 17, 2025, 11:45–12:00, H47
Partition Function Zeros of the Frustrated J1-J2 Ising Model on the Honeycomb Lattice — •Denis Gessert1,2, Martin Weigel3, and Wolfhard Janke1 — 1Institut für Theoretische Physik, Leipzig University, 04081 Leipzig, Germany — 2Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom — 3Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
We study the partition function zeros in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor (J1 > 0) and next-nearest-neighbor (J2 < 0) interactions on the honeycomb lattice. We consider the finite-size scaling (FSS) of the leading Fisher and Lee-Yang zeros as determined from a cumulant method and compare it to a traditional scaling analysis based on the logarithmic derivative of the magnetization ∂ ln⟨ |M| ⟩ /∂β and the magnetic susceptibility χ. While for this model both FSS approaches are subject to strong corrections to scaling induced by the frustration, their behavior is rather different, in particular as the ratio R = J2/J1 is varied. As a consequence, an analysis of the scaling of partition function zeros turns out to be a useful complement to a more traditional FSS analysis. The scaling of the zeros convincingly shows that the system remains in the Ising universality class for R as low as −0.22, where results from traditional FSS using the same simulation data are less conclusive. The approach hence provides a valuable additional tool for mapping out the phase diagram of models afflicted by strong corrections to scaling.
Keywords: Ising model; frustration; partition function zeros; scaling laws; critical exponents