Common Scaling Functions in Dynamical and Quantum Phase Transitions
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In this chapter, based on the phenomenological structure for the large deviation principle, we study the dynamical phase transition taking place in the biased ensemble of time-averaged activity in Kinetically Constrained Models (KCMs). We focus on the mean-field version of these models, and construct an analytical expression of a Hamiltonian corresponding to this dynamical phase transition point. This Hamiltonian itself shows non-analyticity in infinite system size limit, from which the domain of the system variable is divided into two regions, such as active and inactive regions. Furthermore, from this singular Hamiltonian, we construct finite-size scaling functions around the dynamical phase transition point, and show that this functional form is universal between this dynamical phase transition and the quantum phase transition of transverse mean-field Ising model.
KeywordsKinetically constrained models Dynamical phase transition Finite-size scaling in 1st order phase transition Transverse ising model Quantum phase transition
- 3.J.P. Garrahan, P. Sollich, C. Toninelli, (2010) arXiv:1009.6113, which is a chapter in Ref. (L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, W. van Saarloos, (eds.), Dynamical Heterogeneities in Glasses, Colloids, and Granular Media (Oxford University Press, Oxford, 2011))
- 11.V. Bapst, G. Semerjian, J. Stat. Mech. (2012) P06007Google Scholar
- 12.T. Nemoto, V. Lecomte, S. Sasa, F. van Wijland, J. Stat. Mech. (2014) P10001Google Scholar