David Mesterházy

Multicritical behavior in models with two competing order parameters

We employ the nonperturbative functional renormalization group to study models with an O(N(1) ⊕O(N)(2)) symmetry. Here different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N(1),N(2) plane. We study the fate of nontrivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of noncanonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.

Functional renormalization group approach to the Yang-Lee edge singularity

A bstractWe determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 − d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O∂4

Stability of fixed points and generalized critical behavior in multifield models

\mathcal{O}\left({\partial}^4\right)

Solvable Markovian dynamics of lattice quantum spin models

truncations of the scale-dependent effective action.

Dynamics of dissipative Bose-Einstein condensation

We establish new scaling properties for the universality class of Model C, which describes relaxational critical dynamics of a nonconserved order parameter coupled to a conserved scalar density. We find an anomalous diffusion phase, which satisfies weak dynamic scaling while the conserved density diffuses only asymptotically. The properties of the phase diagram for the dynamic critical behavior include a significantly extended weak scaling region, together with a strong and a decoupled scaling regime. These calculations are done directly in 2 < d < 4 space dimensions within the framework of the nonperturbative functional renormalization group. The scaling exponents characterizing the different phases are determined along with subleading indices featuring the stability properties.

Discovering and quantifying nontrivial fixed points in multi-field models

We study models with three coupled vector fields characterized by O(N_{1})⊕O(N_{2})⊕O(N_{3}) symmetry. Using the nonperturbative functional renormalization group, we derive β functions for the couplings and anomalous dimensions in d dimensions. Specializing to the case of three dimensions, we explore interacting fixed points that generalize the O(N) Wilson-Fisher fixed point. We find a symmetry-enhanced isotropic fixed point, a large class of fixed points with partial symmetry enhancement, as well as partially and fully decoupled fixed-point solutions. We discuss their stability properties for all values of N_{1},N_{2}, and N_{3}, emphasizing important differences to the related two-field models. For small numbers of field components, we find no stable fixed-point solutions, and we argue that this can be attributed to the presence of a large class of possible (mixed) couplings in the three-field and multifield models. Furthermore, we contrast different mechanisms for stability interchange between fixed points in the case of the two- and three-field models, which generically proceed through fixed-point collisions.

Critical fluctuations and complex spinodal points

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid–gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e. , and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field for . The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for , the Lee-Yang edge singularities are the closest singularities to the real axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real axis for , in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the expansion, as well as the equation of state of the -symmetric theory at large , are both nontrivially consistent with the conjecture. We analyze the reason for the difficulty of addressing this issue using the e expansion. It is related to the long-standing paradox associated with the fact that the vicinity of the Lee-Yang edge singularity is described by Fisher’s theory, which remains nonperturbative even for , where the equation of state of the theory is expected to approach the mean-field result. We resolve this paradox by deriving the Ginzburg criterion that determines the size of the region around the Lee-Yang edge singularity where mean-field theory no longer applies.

Dissipative Bose–Einstein condensation in contact with a thermal reservoir

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic timescales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.