Self-Maintained Order and Hysteretic Collapse in a Non-Equilibrium Rotational Lattice

Abstract

Version 9, revised for Physica A. A two-dimensional rotor lattice whose ordering couplings are removed by an order-dependent flux and restored by repair. The mean-field reduction is bistable above a computed feedback threshold; version 9 adds a kinetic Monte Carlo study designed to separate static from rate-dependent hysteresis, and finds that the bistability survives on the lattice only when degradation senses order over an extended region. What the Monte Carlo shows. The annealed mean-field reduction of the model is bistable (window 3.92 < ρ < 11.30 at h = 6, K = 0.5, β = 20; threshold βc = 2.42 at h = 6, and no bistability for h ≤ 1). On the lattice with nearest-neighbour feedback it is not. The loop area of ρ sweeps (L = 16–64, nine rates, eight runs) peaks at 2.5 for fast sweeps and is zero within error for dwells of 64 steps or more at every size and in a colder field-free variant; the mean-field static area is 4.30. Ordered and collapsed starts inside the window converge to the same state (within 0.004 in all 40 cases), in 15–115 steps independent of N. The cause is the closure: the lattice applies the average of the steep feedback over a broad distribution of local disorder, which flattens it. With the kill rate sensing wider blocks, the slow-sweep loop area is 0.01, 0.03, 0.21, 1.00 and 1.93 for 4, 8, 24, 80 sites and global sensing, and the two starts split at 80 sites and globally. Bistability is realized when degradation senses order over an extended range. Quenched-dilution finite-size scaling (L = 16–96, eight realizations) places the field-free loss of stiffness at fKT = 0.205 (1/ln2L extrapolation, 95% interval 0.193–0.216) and 0.205 (Weber–Minnhagen, 0.198–0.213), far below site percolation (0.407). Also: an exact order–entropy bridge (dS/dU = −κ for the von Mises law) and the Schnakenberg entropy production of the maintenance cycle. Code, raw data and analysis: https://github.com/sandlerleon/rotational-lattice-maintenance, archived at 10.5281/zenodo.23130923. Version 9 also corrects the discrete-time statement of the β = 0 baseline and the positivity condition of the entropy production (λR > ε2).