Critical exponents can be different on the two sides of a transition: A generic mechanism

Abstract

We present models where ${\gamma }_{+}$ and ${\gamma }_{-}$, the exponents of the susceptibility in the high and low temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete anisotropies that are irrelevant in the renormalization-group sense. The ${\mathbb{Z}}_q$-invariant models are the simplest examples for two-component order parameters ($N=2$) and the icosahedral symmetry for $N=3$. We compute accurately ${\gamma }_{+}-{\gamma }_{-}$ as well as the ratio $\nu /{\nu }^{\prime }$ of the exponents of the two correlation lengths present for $T<T_c$.

References in corpus (6)

• Exact evolution equation for the effective potential
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7
• A Scaling Relation for Dangerously Irrelevant Symmetry-Breaking Fields
• Semiclassical evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice

Cited by in corpus (41)

• The nonperturbative functional renormalization group and its applications
• Quantum criticality with two length scales
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{P}\mathcal{T}$ symmetry to quantum fluctuations
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Phases Of Melonic Quantum Mechanics
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Surface criticality of antiferromagnetic Potts model
• Activating critical exponent spectra with a slow drive
• The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
• Thermodynamics of the two-dimensional XY model from functional renormalization
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Platonic Field Theories
• Surface critical properties of the three-dimensional clock model
• Constraints on discrete global symmetries in quantum gravity
• Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and non-Fermi liquid to Fermi liquid crossover
• Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures
• Mass hierarchy in collective modes of pair-density-wave superconductors
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Anomalous criticality with bounded fluctuations and long-range frustration induced by broken time-reversal symmetry
• Dual dynamic scaling in deconfined quantum criticality
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization
• Current-induced inverse symmetry breaking and asymmetric critical phenomena at current-driven tricritical point
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Non-trivial critical behavior at the magnetic transitions: A case study of Sm${}_7$Pd${}_3$
• A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O($N$) models at large $N$
• Relaxation Critical Dynamics with Emergent Symmetry
• Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
• Janus van der Waals equations for real molecules with two-sided phase transitions
• New Methods for Critical Analysis: Revealing the Simultaneous Existence of Universality Classes in Nontrivial Magnetic Systems