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.

对称破缺在现代物理学中起着举足轻重的作用。尽管自相似性也是一种对称性，并且在自然界中无处不在，但出现了一个基本问题，即自相似性破坏是否有意义。在这里，通过识别一种重要的临界波动类型，称为“相位波动”，并比较具有自相似性和缺乏自相似性的相位波动的数值结果，我们表明自相似性确实可以被打破，至少在非平衡情况下会产生重大后果。我们发现自相似性的破坏会导致新的关键指数，从而违反众所周知的有限大小缩放或不太知名的有限时间缩放，当受到线性加热或冷却通过其临界点的最简单非平衡驱动时，二维或三维有限格上的范式 Ising 模型的有序或无序阶段的不同主要指数。这与通常的临界现象中的相同指数和不同幅度形成鲜明对比。我们的结果证明了驱动的非平衡临界现象是多么令人惊讶。还预计该理论在其他经典和量子相变中的应用。我们的结果证明了驱动的非平衡临界现象是多么令人惊讶。还预计该理论在其他经典和量子相变中的应用。我们的结果证明了驱动的非平衡临界现象是多么令人惊讶。还预计该理论在其他经典和量子相变中的应用。