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Dynamical phase transitions in a random environment

D. Ben-Avraham I. Webman

Philosophical Magazine BMay 1, 19988 citations

Dynamic scaling in diluted systems: Deactivation through thermal dilution

Manuel I. Marqués, Julio A. Gonzalo

Activated scaling is confirmed to hold in transverse field-induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold (pc) but also well below and above it. We follow the evolution of the activated scaling at zero temperature in the phase transition from ferromagnetic to quantum Griffiths phase (p>pc) at the phase boundary (p=pc) and for transitions inside the nonferromagnetic quantum Griffiths phase (p<pc). A novel deactivation phenomenon inside the nonferromagnetic Griffiths-McCoy phase (p<pc) is observed using a thermal (in contrast to random) dilution of the system.Activated scaling is confirmed to hold in transverse field-induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold (pc) but also well below and above it. We follow the evolution of the activated scaling at zero temperature in the phase transition from ferromagnetic to quantum Griffiths phase (p>pc) at the phase boundary (p=pc) and for transitions inside the nonferromagnetic quantum Griffiths phase (p<pc). A novel deactivation phenomenon inside the nonferromagnetic Griffiths-McCoy phase (p<pc) is observed using a thermal (in contrast to random) dilution of the system.

arXiv:cond-mat/0009007Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsApr 18, 20010 citations

Statistical physics and phase transitions

Lorenza Saitta, Attilio Giordana, Antoine Cornuéjols

Cambridge University Press eBooksJun 16, 20110 citations

Mean-field entanglement transitions in random tree tensor networks

Javier Lopez-Piqueres, Brayden Ware, Romain Vasseur

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

arXiv:2003.01138Physical review. B./Physical review. BAug 6, 202071 citations

Phase Transitions on Random Lattices: How Random is Topological Disorder?

Hatem Barghathi, Thomas Vojta

We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω=(d-1)/(2d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d+1)ν>2 rather than the usual Harris criterion dν>2, making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d>1. These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices.We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω=(d-1)/(2d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d+1)ν>2 rather than the usual Harris criterion dν>2, making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d>1. These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices.

arXiv:1402.4425Physical Review LettersSep 19, 201440 citations

Phase Transitions and the Scaling Hypothesis

Peter Kopietz, Lorenz Bartosch, Florian Schütz

Lecture notes in physicsDec 25, 20090 citations

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