Self-Similarity Breaking: Anomalous Nonequilibrium Finite-Size Scaling and Finite-Time Scaling

Symmetry breaking plays a pivotal role in modern physics. Although self-similarity is also a symmetry, and appears ubiquitously in nature, a fundamental question arises as to whether self-similarity breaking makes sense or not. Here, by identifying an important type of critical fluctuation, dubbed 'phases fluctuations', and comparing the numerical results for those with self-similarity and those lacking self-similarity with respect to 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, giving rise to a violation of the well-known finite-size scaling, or the less well-known finite-time scaling, and different leading exponents in either the ordered or the disordered phases of the paradigmatic Ising model on two- or three-dimensional finite lattices, when subject to the simplest nonequilibrium driving of linear heating or cooling through its critical point. This is in stark contrast to identical exponents and different amplitudes in usual critical phenomena. Our results demonstrate how surprising driven nonequilibrium critical phenomena can be. The application of this theory to other classical and quantum phase transitions is also anticipated.