Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study

Abstract

We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting universality classes by combining transfer matrix data with conformal invariance. The magnetic exponent beta/nu varies continuously with q, assuming non-Ising values for q>4, whereas the correlation length exponent nu is numerically consistent with unity. We present evidence for the correctness of a formerly proposed phase diagram, unifying pure, percolative and non-trivial random behaviour.

25 pages of RevTeX, 7 ps-figures. Submitted to Nucl. Phys. B

References in corpus (5)

• Critical Behavior of Random Bond Potts Models
• Revisiting the Theory of Finite Size Scaling in Disordered Systems: νCan Be Less Than 2/d
• Weak Randomness for large q-State Potts models in Two Dimensions
• New sum rule identities and duality relation for the Potts $n$-point correlation function
• Duality Relations for Potts Correlation Functions

Cited by in corpus (102)

• Large-q asymptotics of the random bond Potts model
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Nishimori point in the 2D +/- J random-bond Ising model
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond $d=2$ Blume-Capel model
• Quenched Randomness at First-Order Transitions
• Monte Carlo Study of the Critical Behavior of Random Bond Potts Models
• Field theory of compact polymers on the square lattice
• Bond dilution in the 3D Ising model: a Monte Carlo study
• Spanning forests and the q-state Potts model in the limit q \to 0
• Universality, frustration and conformal invariance in two-dimensional random Ising magnets
• Evidence for softening of first-order transition in 3D by quenched disorder
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• Monte Carlo Study of Phase Transitions in the Bond-Diluted 3D 4-State Potts Model
• Critical behaviour of the 2d spin diluted Ising model via the equilibrium ensemble approach
• Curvature-driven coarsening in the two dimensional Potts model
• Coupled Potts models: Self-duality and fixed point structure
• Strong disorder fixed points in the two-dimensional random-bond Ising model
• Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries
• Universality and multifractal behaviour of spin-spin correlation functions in disordered Potts models
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Tests of Conformal Invariance in Randomness Induced Second-Order Phase Transitions
• First order transition in a three dimensional disordered system
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models II. Extended Results for Square-Lattice Chromatic Polynomial
• Simulation of Potts models with real q and no critical slowing down
• Critical manifold of the kagome-lattice Potts model
• Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points
• Transfer matrix computation of critical polynomials for two-dimensional Potts models
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Emerging criticality in the disordered three-color Ashkin-Teller model
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
• Critical interfaces in the random-bond Potts model
• Disorder induced rounding of the phase transition in the large q-state Potts model
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Universality in disordered systems: The case of the three-dimensional random-bond Ising model
• Fidelity Threshold of the Surface Code Beyond Single-Qubit Error Models
• Symmetry relation for multifractal spectra at random critical points
• Exact results for quenched bond randomness at criticality
• The Random-bond Potts model in the large-q limit
• Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder
• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• Phase diagram and critical exponents of a Potts gauge glass
• Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Disorder driven phase transitions of the large q-state Potts model in 3d
• On superuniversality in the $q$-state Potts model with quenched disorder
• Multiscaling of energy correlations in the random-bond Potts model
• Quenched bond dilution in two-dimensional Potts models
• Bond disorder induced criticality of the three-color Ashkin-Teller model
• Ising and Potts Models on Quenched Random Gravity Graphs
• A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation
• Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits
• Directed polymer in a random medium of dimension 1+3 : multifractal properties at the localization/delocalization transition
• Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions
• On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder
• The effect of quenched bond disorder on first-order phase transitions
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Wang-Landau study of the 3D Ising model with bond disorder
• Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions
• On the phase diagram of the random bond $q$-state Potts model
• Correlated correlation functions in random-bond ferromagnets
• Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions
• Critical Behavior of the Random Potts Chain
• Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions
• Phase-transitions of the random bond Potts chain with long-range interactions
• Level repulsion exponent $\beta$ for Many-Body Localization Transitions and for Anderson Localization Transitions via Dyson Brownian Motion
• Random Defect Lines in Conformal Minimal Models
• Long-range quenched bond disorder in the bi-dimensional Potts model
• Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization
• Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain
• Random cascade models of multifractality : real-space renormalization and travelling-waves
• Non compact continuum limit of two coupled Potts models
• Statistical mechanics of high-density bond percolation
• New correlation duality relations for the planar Potts model
• Properties of the multicritical point of +/- J Ising spin glasses on the square lattice
• Correlation length-exponent relation for the two-dimensional random Ising model
• Critical Properties of Weak Measurement Induced Phase Transitions in Random Quantum Circuits
• Infinite disorder and correlation fixed point in the Potts model with correlated disorder
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Density of critical clusters in strips of strongly disordered systems
• Phase diagram and the strong-coupling fixed point in the disordered O(n) loop model
• Corrections to scaling in the dynamic approach to the phase transition with quenched disorder
• Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line
• Influence of aperiodic modulations on first-order transitions: numerical study of the two-dimensional Potts model
• Statistics of geometric clusters in the Ising model on a Bethe lattice: statistical mechanics approach
• Nishimori point in random-bond Ising and Potts models in 2D
• Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models
• $U_{\mathfrak{q}}({\mathfrak{sl}}_3)$ web models: Locality, phase diagram and geometrical defects
• Emerging critical behavior at a first-order phase transition rounded by disorder
• Two-dimensional O(n) model in a staggered field
• Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach
• Further evidence of the absence of Replica Symmetry Breaking in Random Bond Potts Models
• Critical behavior of loops and biconnected clusters on fractals of dimension d < 2
• Inhomogeneities on all scales at a phase transition altered by disorder
• Statistics of geometric clusters in Potts model: statistical mechanics approach
• Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit
• Smeared spin-flop transition in random antiferromagnetic Ising chain
• Interface mapping in two-dimensional random lattice models
• Coulomb Gas Partition Function of a Layered Loop Model