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Universal scaling laws form one of the central issues in physics. A non-standard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a non-standard scaling law with respect to system size in a synchronized state of globally coupled non-identical phase oscillators [Nishikawa et al., Chaos $boldsymbol{22}$, 013133 (2012)]. However, it is still unclear how widely this non-standard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems, and we validate the conditions by numerical simulations of several different models.
We investigate a critical exponent related to synchronization transition in globally coupled nonidentical phase oscillators. The critical exponents of susceptibility, correlation time, and correlation size are significant quantities to characterize f
We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its mean valu
The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/alpha}$ with the size of the subsystem $L$, here
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard formulations of fi