We study the q-state Potts model for q and the space dimension d arbitrary real numbers using the derivative expansion of the nonperturbative renormalization group at its leading order, the local potential approximation (LPA and LPA^{'}). We determine the curve q_{c}(d) separating the first [q>q_{c}(d)] and second [q
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http://dx.doi.org/10.1103/PhysRevE.108.064120 DOI Listing Publication Analysis
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Phys Rev E
October 2024
Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg.
We prove a linear stability-dissipation relation (SDR) for q-state Potts models driven far from equilibrium by a nonconservative force. At a critical coupling strength, these models exhibit a synchronization transition from a decoherent into a synchronized state. In the vicinity of this transition, the SDR connects the entropy production rate per oscillator to the phase-space contraction rate, a measure of stability, in a simple way.
View Article and Find Full Text PDFPhys Rev E
October 2024
Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg.
We study driven q-state Potts models with thermodynamically consistent dynamics and global coupling. For a wide range of parameters, these models exhibit a dynamical phase transition from decoherent oscillations into a synchronized phase. Starting from a general microscopic dynamics for individual oscillators, we derive the normal form of the high-dimensional Hopf bifurcation that underlies the phase transition.
View Article and Find Full Text PDFPhys Rev E
August 2024
Center for Complex Systems, KI of Grid Modernization, Korea Institute of Energy Technology, Naju, Jeonnam 58330, Korea.
A hidden state in which a spin does not interact with any other spin contributes to the entropy of an interacting spin system. We explore the q-state Potts model with extra r hidden states using the Ginzburg-Landau formalism in the mean-field limit. We analytically demonstrate that when 1 View Article and Find Full Text PDF
Phys Rev Lett
August 2024
CNRS-Laboratoire de Physique de l'Ecole Normale Supérieure, PSL Research University, Sorbonne Université, Université Paris Cité, 24 rue Lhomond, 75005 Paris, France.
The two-dimensional Q-state Potts model with real couplings has a first-order transition for Q>4. We study a loop-model realization in which Q is a continuous parameter. This model allows for the collision of a critical and a tricritical fixed point at Q=4, which then emerge as complex conformally invariant theories at Q>4, or even complex Q, for suitable complex coupling constants.
View Article and Find Full Text PDFCommun Math Phys
August 2024
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978 Israel.
The Imry-Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin systems are 'rounded' by the addition of a quenched random field coupled to the quantity undergoing the transition. The phenomenon applies to a wide class of spin systems in dimensions and to spin systems possessing a continuous symmetry in dimensions . This work provides quantitative estimates for the Imry-Ma phenomenon: in a cubic domain of side length , we study the effect of the boundary conditions on the spatial and thermal average of the quantity coupled to the random field.
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