Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.37436

Phase separation, morphology, and metastability in the three-dimensional active Potts model

Aditya Kumar Dutta·Raja Paul
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the three-dimensional active Potts model (APM) on a cubic lattice with 2, 4, and 6 orientational states. The steady-state phase diagrams exhibit low-density gaseous, high-density polar liquid, and liquid--gas coexistence phases, with the phase behavior controlled by density, temperature, and propulsion speed and retaining the main features of the previously studied two-dimensional APM. At weak propulsion, the dense phase forms a slab perpendicular to its direction of motion. With increasing propulsion speed, this morphology persists for the 2-state model, whereas the dense phases for 4 and 6 states reorient and propagate along their longitudinal direction. For the 6-state model, the reoriented dense phase further develops a cylindrical morphology. We also examine the stability of polar liquids against artificially introduced droplets using microscopic simulations and coarse-grained hydrodynamic equations. At high propulsion speeds, counter-propagating droplets can partially modify the initial polar state, while transverse droplets can completely alter it, demonstrating the metastable nature of polar liquids in the three-dimensional active Potts model.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Aditya Kumar Dutta, Raja Paul. 2026-09-29. Phase separation, morphology, and metastability in the three-dimensional active Potts model. https://arxiv.org/abs/2609.37436

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Explosive connectivity and mechanical rigidity in cubic lattice structures

We study explosive connectivity and mechanical rigidity in three-dimensional cubic lattice structures under Achlioptas-type product-rule dynamics. Our work combines extensive numerical simulation with a theoretical framework based on rigorous finite-size scaling. Using massive-scale simulations up to $L=192$ ($N \approx 7 \times 10^6$) with 20,000 independent realizations, we demonstrate that for $k \ge 8$, the peak susceptibility scales with an exponent of $γ= 1.000$, and the maximum single-step jump stabilizes at a macroscopic fraction. This confirms that while the transition is continuous in the infinite thermodynamic limit, it exhibits the exact finite-size scaling signatures of a first-order discontinuity in finite physical systems. For rigidity, we discover numerically that for richly-connected hosts, increasing the number of choices $k$ optimally enhances the efficiency of rigidification. To explain this phenomenon, we propose a theoretical model centered on a conditional progress function that links an edge's local product-rule score to its global mechanical utility. We show that while local rigidification efficiency monotonically increases, the global rigidity gap exhibits a ``Goldilocks'' minimum at intermediate $k$ due to the emergence of maximally floppy, tree-like components at large $k$. Altogether, our work provides new insights into the relationship between local dynamics and global connectivity and rigidity in cubic lattice structures via both theory and computation.

cond-mat.stat-mech↗
arXiv2026

Sticky eigenstates in systems with sharply divided phase space

We investigate mixed eigenstates in systems with sharply divided phase space, using different piecewise-linear maps whose regular-chaotic boundaries are formed by marginally unstable periodic orbits (MUPOs) or by quasi-periodic orbits. With the overlap index and the entropy localization length, we classify mixed eigenstates and show that the contribution from dynamical tunneling scales as $\sim \hbar\, \exp(-b/\hbar)$, with $b>0$ associated with the relative size of the regular region. The dominant fraction of states that remain sticky to the boundaries, referred to as sticky eigenstates, scales approximately as $\hbar^{1/2}$ in the MUPO case and oscillates around this algebraic behavior in the quasiperiodic case. This behavior generalizes established predictions for hierarchical states in Kolmogorov-Arnold-Moser (KAM) systems, which scale as $\hbar^{1 - 1/γ}$, with $γ$ set by the corresponding classical stickiness reflected in the algebraic decay of cumulative recurrence-time distributions $t^{-γ}$. For the piecewise-linear maps studied here, $γ= 2$. These results reveal a clear quantum signature of classical stickiness in non-KAM systems.

cond-mat.stat-mech↗
arXiv2026

Matrix-Product Belief Propagation for continuous-state-space variables

Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is fundamental for a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of such observables in tree-like networks with a controlled error that depends on the bond dimension, that is the dimension of the employed square matrices. Its computational cost is linear in the time horizon and the network size for a large family of models with discrete degrees of freedom. Here, a generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis. For a wide class of models, the computational cost of the method is linear in the network size with a prefactor that depends on the basis size and the bond dimension. The method's efficacy is demonstrated by employing a Fourier basis for a mixed continuous/discrete representation of the Kinetic Ising dynamics with real-valued random couplings, where intermediate "local fields" are treated as continuous. The accuracy of the method is verified via comparison with Monte Carlo simulations. For this model, we calculate time auto-correlations, time evolution of energy and magnetization, and finally we estimate the large deviation function of the magnetization at a given future time.

cond-mat.stat-mech↗