From Thermodynamically Driven Phase Transitions to Quantum Critical Phenomena

Amit Dutta, Chakrabarti, B K

Uwe Claus Täuber

Originally, the term ‘dynamic critical phenomena’ was coined for time-dependent properties near second-order phase transitions in thermal equilibrium . The kinetics of phase transitions in magnets, at the gas–liquid transition, and at the normal- to superfluid phase transition in helium 4 were among the prominent examples investigated already in the 1960s. The dynamic scaling hypothesis , generalizing the scaling ansatz for the static correlation function and introducing an additional dynamic critical exponent, successfully described a variety of these experiments. Yet only the development of the systematic renormalization group (RG) approach for critical phenomena in the subsequent decade provided a solid conceptual foundation for phenomenological scaling theories. Supplemented with exact solutions for certain idealized model systems, and guided by invaluable input from computer simulations in addition to experimental data, the renormalization group now provides a general framework to explore not only the static and dynamic properties near a critical point, but also the large-scale and low-frequency response in stable thermodynamic phases. Scaling concepts and the renormalization group have also been successfully applied to phase transitions at zero temperature driven by quantum rather than thermal fluctuations. It is to be hoped that RG methods may help to classify the strikingly rich phenomena encountered in far-from-equilibrium systems as well. Recent advances in studies of simple reaction-diffusion systems, active to absorbing state phase transitions, driven lattice gases, and scaling properties of moving interfaces and growing surfaces, among others, appear promising in this respect.

Masatoshi Imada

Alessandro Coppo, Aanal Jayesh Shah, Hadiseh Alaeian +3 more

Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce $nonlocal$ $quantum$ $fluctuations$ as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.

Erol Vatansever, Mikel Quintana, Andreas Berger

We investigate the crossover of critical behavior for the dynamic phase transition (DPT) in ferromagnetic thin films using Monte Carlo simulations of the kinetic Ising model, focusing on the scaling behavior of the dynamic order parameter under a time-dependent external magnetic field. Specifically, we study the transition of the critical behavior of such multilayer film systems from two-dimensional (2D) to three-dimensional (3D) as a function of the film thickness and the distance to the critical point, which enables dimensional crossover observations. Our results indicate that the effective critical exponents exhibit a clear transition in their scaling behavior, with thinner films showing 2D-like characteristics and thicker films displaying 3D-like behavior, for both the DPT and the thermodynamic phase transitions (TPT). Quantitatively, the crossover from 2D to 3D behavior occurs at larger film thicknesses for the DPT compared to the TPT, suggesting that DPT and TPT are governed by distinctly different length scales and underlying surface effects. These findings are in agreement with experimental observations in ultrathin Co films, where dynamic and thermodynamic critical exponents were found to differ. Therefore, our study provides an in-depth explanation for critical phenomena in thin-film ferromagnets driven by a time-dependent magnetic field. By comparing the dimensional crossover properties of both TPT and DPT, we present a comprehensive understanding of how thin-film geometry and surface effects influence the scaling laws and critical behavior in nonequilibrium systems.

David R. Nelson