For the two-dimensional $Q$ -state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number ${N}_{\ensuremath{\Gamma}}$ of clusters that intersect a given contour $\ensuremath{\Gamma}$. To leading order, ${N}_{\ensuremath{\Gamma}}$ is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of $\ensuremath{\Gamma}$. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.For the two-dimensional $Q$-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number ${N}_{\ensuremath{\Gamma}}$ of clusters that intersect a given contour $\ensuremath{\Gamma}$. To leading order, ${N}_{\ensuremath{\Gamma}}$ is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of $\ensuremath{\Gamma}$. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.

arXiv:1311.4186Physical Review BFeb 24, 201411 citations

Clusters and phase transitions

Boris Michailovich Smirnov

Uspekhi Fizicheskih NaukJan 1, 200723 citations

Dynamics of Clusters in Three-Dimensional 3-State Potts Model

Fatih Yaşar, Y. Gündüç, Meral Aydın +1 more

Dynamical evaluation of the observables changing per iteration in a Monte Carlo simulation possess vital information about the order of the phase transition occuring in the system ~[1]. Being a global operator, average cluster size is a good candidate to study the order of the phase transition. It is expected that study of cluster dynamics yields indicative information ~[1-3]. In this work cluster algorithm ~[4,5] is used to study the dynamical behavior of the average cluster size in $3$ -dimensional 3-state Potts model ~[6] which is known to exhibit weak first-order transition ~[7]. Cluster size is calculated as the average of 1000 or higher replicas at each Monte Carlo iteration, during first few hundred iterations. Results for different sizes show the first-order character of the phase transition occuring in the model without performing time consuming computations to calculate the equilibrium averages.Dynamical evaluation of the observables changing per iteration in a Monte Carlo simulation possess vital information about the order of the phase transition occuring in the system ~[1]. Being a global operator, average cluster size is a good candidate to study the order of the phase transition. It is expected that study of cluster dynamics yields indicative information ~[1-3]. In this work cluster algorithm ~[4,5] is used to study the dynamical behavior of the average cluster size in $3$-dimensional 3-state Potts model ~[6] which is known to exhibit weak first-order transition ~[7]. Cluster size is calculated as the average of 1000 or higher replicas at each Monte Carlo iteration, during first few hundred iterations. Results for different sizes show the first-order character of the phase transition occuring in the model without performing time consuming computations to calculate the equilibrium averages.

TURKISH JOURNAL OF PHYSICSJan 1, 19970 citations

Cluster expansion of operator averages for systems of many particles

João da Providência

Nuclear PhysicsJul 1, 196323 citations

The Dynamical Cluster Approximation

Mark Jarrell

Bulletin of the American Physical SocietyMar 21, 20051 citation

Dynamical quantum phase transitions in Sachdev-Ye-Kitaev Lindbladians

Kohei Kawabata, Anish Kulkarni, Jiachen Li +2 more

We study the open quantum dynamics of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Of particular interest for us is the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo. We find that the dissipative form factor exhibits dynamical quantum phase transitions. We analytically demonstrate a discontinuous dynamical phase transition in the limit of a large number of fermion flavors, which is formally akin to the thermal phase transition in the two-coupled SYK model between the black-hole and wormhole phases. We also find continuous dynamical phase transitions that do not have counterparts in the two-coupled SYK model. While the phase transitions are sharp in the limit of a large number of fermion flavors, their qualitative signatures are present even for a finite number of fermion flavors, as we show numerically.We study the open quantum dynamics of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Of particular interest for us is the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo. We find that the dissipative form factor exhibits dynamical quantum phase transitions. We analytically demonstrate a discontinuous dynamical phase transition in the limit of a large number of fermion flavors, which is formally akin to the thermal phase transition in the two-coupled SYK model between the black-hole and wormhole phases. We also find continuous dynamical phase transitions that do not have counterparts in the two-coupled SYK model. While the phase transitions are sharp in the limit of a large number of fermion flavors, their qualitative signatures are present even for a finite number of fermion flavors, as we show numerically.

arXiv:2210.04093Physical review. B./Physical review. BAug 3, 202343 citations

For the two-dimensional

Q

-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number ${N}_{\ensuremath{\Gamma}}$ of clusters that intersect a given contour $\ensuremath{\Gamma}$. To leading order, ${N}_{\ensuremath{\Gamma}}$ is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of $\ensuremath{\Gamma}$. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.

3

-dimensional 3-state Potts model ~[6] which is known to exhibit weak first-order transition ~[7]. Cluster size is calculated as the average of 1000 or higher replicas at each Monte Carlo iteration, during first few hundred iterations. Results for different sizes show the first-order character of the phase transition occuring in the model without performing time consuming computations to calculate the equilibrium averages.