Markov length can diverge in systems whose universal physics is spatially Markovian

arXiv:2610.11235 · cond-mat.stat-mech, cond-mat.str-el, quant-ph · Submitted 2026-10-08 · Read on arXiv

cond-mat.stat-mech, cond-mat.str-el, quant-ph

Submitted: 2026-10-08

Updated: 2026-10-08

Terminology

• Entanglement — 10× in this paper · explained in 3 episodes
• Gibbs State — 10× in this paper · explained in 2 episodes
• Entanglement Entropy — 8× in this paper · explained in 2 episodes
• Langevin Dynamics — 4× in this paper · explained in 2 episodes
• Anisotropy — 2× in this paper · explained in 3 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Frustration — 1× in this paper · explained in 2 episodes
• Non-Markovianity — 1× in this paper · explained in 3 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Quantum Markov Networks and Commuting Hamiltonians
• Mixed-state phases from local reversibility
• Generic long-range correlations in nonequilibrium mixtures
• Non-perturbative constraints on stability and renormalization group flows in nonequilibrium matter
• Diverging conditional correlation lengths in the approach to high temperature
• Squeezing codes: robust fluctuation-stabilized memories
• Topological Mixed States: Phases of Matter from Axiomatic Approaches
• On the asymptotics of a Toeplitz determinant with singularities

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