Abstract Phase transitions in condensed matter are a source of exotic emergent properties. We study the fully frustrated bilayer Heisenberg antiferromagnet to demonstrate that an applied magnetic field creates a previously unknown emergent criticality. The quantum phase diagram contains four states with distinctly different symmetries, all but one pair separated by first-order transitions. We show by quantum Monte Carlo simulations that the thermal phase diagram is dominated by a wall of discontinuities extending between the dimer-triplet phases and the singlet-containing phases. This wall is terminated at finite temperatures by a critical line, which becomes multicritical where the Berezinskii-Kosterlitz-Thouless (BKT) transition of the dimer-triplet antiferromagnet and the thermal Ising transition of the singlet-triplet crystal phase also terminate. The combination of merging symmetries leads to a 4-state Potts universality not contained in the microscopic Hamiltonian, which we interpret within the Ashkin-Teller model. Our results represent a systematic step in understanding emergent phenomena in quantum magnetic materials, including the “Shastry-Sutherland compound” SrCu2(BO3)2.
Critical point of liquid-gas (LG) transition does not conform with the paradigm of spontaneous symmetry breaking because there is no broken symmetry in both phases. We revisit the conjecture that this critical point belongs to the Ising class by performing large scale Monte Carlo simulations in two-dimensional free space in combination with the numerical flowgram method. Our main result is that the critical indices do agree with the Onsager values within the error of 1%-2%. This significantly improves the accuracy reported in the literature. The related problem about the role of higher order odd terms in the (real) φ^{4} field model as a mapping of the LG transition is addressed too. The scaling dimension of the φ^{5} term at criticality is shown to be the same as that of the linear one φ. We suggest that the role of all higher order odd terms at criticality is simply in generating the linear field operator with the critical dimension consistent with the Ising universality class.
We consider the finite-temperature phase diagram of the S=1/2 frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of first-order transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer and the dimer-singlet state terminates on the first-order line, giving a quantum critical end point, and we use tensor-network calculations to follow the first-order discontinuities in its vicinity.
Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts.However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin.In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior.Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high-to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase.Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z 2 symmetry.However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a Z 2 × Z 2 symmetry.Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system.We elucidate various exotic features of these NEFPs.In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance.This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition.As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths.Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.
Recently, the ordering scenario of three-dimensional site frustrated Heisenberg models has been challenged. The existence of a decoupled tetracritical point (DTP) where ferromagnetic (FM) and antiferromagnetic (AF) order occur simultaneously has been modified to include a line of multicritical points where both FM and AF occur simultaneously. In addition, numerous studies claim that, within the mixed phase, critical exponents are altered from Heisenberg values. Here we show that within the narrow region of proposed multicritical points, the transition temperatures away from the tetracritical point are indeed distinct, confirming the occurrence of a DTP. In addition, we show a universal scaling collapse of the magnetization both away from, and within, the mixed phase using Heisenberg exponents, demonstrating that the stable fixed points are within the Heisenberg universality class.
We consider the thermal phase transition from a paramagnetic to a stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions
J1<0 (nearest neighbor, ferromagnetic) and
J2>0 (second neighbor, antiferromagnetic). The striped phase breaks a
Z4 symmetry and is stabilized at low temperatures for
g=J2/∣J1∣>1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [Phys. Rev. Lett. 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The
J1-
J2 model has a line of very weak first-order phase transitions in the whole region
1/2<g<g∗, where ${g}^{*}=0.67\ifmmode\pm\else\textpm\fi{}0.01$. Thereafter, the transitions from
g=g∗ to $g\ensuremath{\rightarrow}\ensuremath{\infty}$ are continuous and can be fully mapped, using universality arguments, to the critical line of the well-known Ashkin-Teller model from its four-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point
g∗ in the
J1-
J2 model. The continuous transitions near
g∗ can therefore be mistaken for first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of
g>1/2. Most of our conclusions are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.