Self-similarity breaking: Anomalous nonequilibrium finite-size scaling and finite-time scaling

Abstract

Symmetry breaking plays a pivotal role in modern physics. Although self-similarity is also a symmetry and appears ubiquitously in nature, a fundamental question is whether self-similarity breaking makes sense or not. Here, by identifying the most important kind of critical fluctuations dubbed as phases fluctuations and comparing the consequences of having self-similarity with those of lacking self-similarity in the phases fluctuations, we show that self-similarity can indeed be broken with significant consequences at least in nonequilibrium situations. We find that the breaking of self-similarity results in new critical exponents which give rise to violation of the well-known finite-size scaling or the less-known finite-time scaling and different leading exponents in the ordered and the disordered phases of the paradigmatic Ising model on two- or three-dimensional finite lattices when it subjects to the simplest nonequilibrium driving of linear heating or cooling through its critical point, in stark contrast to identical exponents and different amplitudes in usual critical phenomena. Our results demonstrate how surprising driven nonequilibrium critical phenomena can be. Application to other classical and quantum phase transitions is highly expected.

arXiv comment5 pages, 4 figures

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• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Complete universal scaling in first-order phase transitions
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Theory of Critical Phenomena with Memory
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Complete universal scaling of first-order phase transitions in the two-dimensional Ising model