Detecting signals of weakly first-order phase transitions in two-dimensional Potts models

Abstract

We investigate the first-order phase transitions of the $q$-state Potts models with $q=5,6,7$, and $8$ on the two-dimensional square lattice, using Monte Carlo simulations. At the very weakly first-order transition of the $q=5$ system, the standard data-collapse procedure for the order parameter, carried out with results for a broad range of system sizes, works deceptively well and produces non-trivial critical exponents different from the trivial values expected for first-order transitions. However, a more systematic study reveals significant drifts in the `pseudo-critical' exponents as a function of the system size. For this purpose, we employ two methods of analysis: the data-collapse procedure with narrow range of the system size, and the Binder-cumulant crossing technique for pairs of system sizes. In both methods, the estimates start to drift toward the trivial values as the system size used in the analysis exceeds a certain `cross-over' length scale. This length scale is remarkably smaller than the correlation length at the transition point for weakly first-order transitions, e.g., less than one tenth for $q=5$, in contrast to the naive expectation that the system size has to be comparable to or larger than the correlation length to observe the correct behavior. The results overall show that proper care is indispensable to diagnose the nature of a phase transition with limited system sizes.

arXiv comment10 pages, 7 figures. One figure has been replaced to make our claim clearer

References in corpus (18)

• "Deconfined" quantum critical points
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Computational Studies of Quantum Spin Systems
• Deconfined quantum critical points: symmetries and dualities
• Quantum criticality with two length scales
• Walking, Weak first-order transitions, and Complex CFTs
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study
• Quantum criticality in SU(3) and SU(4) anti-ferromagnets
• Dynamics of Weak First Order Phase Transitions
• Kernel method for corrections to scaling
• Calculation of higher-order moments by higher-order tensor renormalization group
• Monte Carlo study of the Pure and Dilute Baxter-Wu model
• Crossover Behavior from Decoupled Criticality
• Scaling in the vicinity of the four-state Potts fixed point

Cited by in corpus (37)

• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Unsupervised learning universal critical behavior via the intrinsic dimension
• Consistent scaling exponents at the deconfined quantum-critical point
• Calculation of higher-order moments by higher-order tensor renormalization group
• Fidelity as a probe for a deconfined quantum critical point
• Shadow of complex fixed point: Approximate conformality of Q>4 Potts model
• Susceptibility anisotropy and its disorder evolution in models for Kitaev materials
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Fixed point annihilation for a spin in a fluctuating field
• A learning by confusion approach to characterize phase transitions
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory
• Deep learning lattice gauge theories
• Multi-impurity method for the bond-weighted tensor renormalization group
• Complete universal scaling in first-order phase transitions
• Non-monotonic behavior of the Binder Parameter in the discrete spin systems
• Metastability in the Potts model: exact results in the large q limit
• Complex entanglement entropy for complex conformal field theory
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows
• Probing phase transitions with correlations in configuration space
• Neural Network Approach to Scaling Analysis of Critical Phenomena
• Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry
• Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger Model and its relevance to Graphene
• Emergent topological ordered phase for the Ising-XY Model revealed by cluster-updating Monte-Carlo method
• Anisotropic deformation of the 6-state clock model: Tricritical-point classification
• Bandwidth controlled quantum phase transition between an easy-plane quantum spin Hall state and an s-wave superconductor
• Extracting partition function zeros from Fukui-Todo simulations
• Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions
• Nematic Antiferromagnetism and Deconfined Criticality from the Interplay between Electron-Phonon and Electron-Electron Interactions
• Quantum criticality at finite temperature for two-dimensional $J{Q}_3$ models on the square and the honeycomb lattices
• Vertex Representation of Hyperbolic Tensor Networks
• Dynamic modes of active Potts models with factorizable numbers of states
• Ultrafast light-induced long range antiferromagnetic correlations in paramagnets
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains