Metastability in the Potts model: exact results in the large <i>q</i> limit

Mazzarisi, Onofrio; Corberi, Federico; Cugliandolo, Leticia F.; Picco, Marco

doi:10.1088/1742-5468/ab8556

Cited by 8 publications

(30 citation statements)

References 44 publications

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“…[4]). The energy density em in the metastable state was computed in [34] and goes to zero for large q as em −a(T )q −1/2 , where a(T ) > 0 is a temperature dependent factor. On the other hand the asymptotic equilibrium quantity e(∞) < 0 becomes independent on q [52] for large q.…”

Section: The Dynamical Processmentioning

confidence: 99%

“…This intriguing feature, which has no analog in the discontinuous field-driven transition of the Ising model, poses yet unresolved questions on the nature of the metastable state in the thermodynamic limit. In a previous paper [34], some of us addressed this problem analytically with a perturbation scheme valid for large q. It turns out that, for q → ∞, a long lived metastable state exists for quenches to final temperatures T > T , where T → Tc/2.…”

Section: Introductionmentioning

confidence: 99%

“…It turns out that, for q → ∞, a long lived metastable state exists for quenches to final temperatures T > T , where T → Tc/2. In [34] a rather precise description of the metastable state was given, both from the microscopic and thermodynamic points of view. However, a similar characterisation of the escape kinetics is still missing for finite q.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we study the process whereby the disordered metastable state is run away and how the target equilibrium state is approached in the square lattice Potts model with q > 4, after shallow quenches from high to low temperatures close to Tc. We use Monte Carlo numerical simulations with the Metropolis rule for different values of q and linear system sizes L. We choose q values which are larger than 4, q = 9, 24, 100, but not too large so that we can observe nucleation in a relatively wide temperature interval below Tc, see [34]. In a companion paper by some of us [35] the related issue of deep quenches below the pseudo-spinodal of the same model for much larger q values, closer to the ideal q → ∞ limit, is tackled and the full parameter dependence of the curvature-driven growing length in the coarsening regime is determined.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

How many phases nucleate in the bidimensional Potts model?

Corberi¹,

Cugliandolo²,

Esposito³

et al. 2021

Preprint

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We study the kinetics of the two-dimensional q > 4-state Potts model after a shallow quench slightly below the critical temperature and above the pseudo spinodal. We use numerical methods and we focus on intermediate values of q, 4 < q ≤ 100. We show that, initially, the system evolves as if it were quenched to the critical temperature. The further decay from the metastable state occurs by nucleation of k out of the q possible phases. For a given quench temperature, k is a logarithmically increasing function of the system size. This unusual finite size dependence is a consequence of a scaling symmetry underlying the nucleation phenomenon for these parameters.

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Section: The Dynamical Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

How many phases nucleate in the bidimensional Potts model?

Corberi¹,

Cugliandolo²,

Esposito³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this paper, and in an accompanying manuscript [37], we build upon the analysis of metastability in the large q bidimensional ferromagnetic Potts model presented in Ref. [38]. In short, we study the dynamical behaviour after a rapid quench for sufficiently large q so that the transition is of first order.…”

Section: Introductionmentioning

confidence: 99%

Low-temperature universal dynamics of the bidimensional Potts model in the large q limit

Chippari,

Cugliandolo,

Picco

2021

Preprint

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We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of large number of states, q 1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account dynamic scaling is universal.

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The two upper critical dimensions of the Ising and Potts models

Wiese,

Jacobsen

2024

J. High Energ. Phys.

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We derive the exact actions of the Q-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless Q-component scalar field Φα. For the Ising model (Q = 2), the field theory for the spins has upper critical dimension $${d}_{{\text{c}}}^{{\text{spin}}}$$ = 4, whereas for the clusters it has $${d}_{{\text{c}}}^{{\text{cluster}}}$$ = 6. As a consequence, the probability for three points to be in the same cluster is not given by mean-field theory for d within 4 < d < 6. We estimate the associated universal structure constant as $$C=\sqrt{6-d}+\mathcal{O}{\left(6-d\right)}^{3/2}$$. This shows that some observables in the Ising model have an upper critical dimension of 4, while others have an upper critical dimension of 6. Combining perturbative results from the ϵ = 6 – d expansion with a non-perturbative treatment close to dimension d = 4 allows us to locate the shape of the critical domain of the Potts model in the whole (Q, d) plane.

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Metastability in the Potts model: exact results in the large q limit

Cited by 8 publications

References 44 publications

How many phases nucleate in the bidimensional Potts model?

How many phases nucleate in the bidimensional Potts model?

Low-temperature universal dynamics of the bidimensional Potts model in the large q limit

The two upper critical dimensions of the Ising and Potts models

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