Periodic planar lattices are built via iterative triangulation to have arbitrarily high Ising critical temperatures, with Tc scaling as (2/ln2) ln q_max and Apollonian lattices conjectured optimal.
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Rigorous proof establishes entropic order in generalized Ising models for p ≥ 1 and demonstrates they solve the NP-hard maximum independent set problem, leading to entropic glass phases.
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
Coupling to mesoscopic reservoirs generates temperature-increasing entropic barriers that suppress topological defect creation and transport, yielding three-regime correlation lengths in 1D Ising chains and double error reduction in finite-size 2D toric codes.
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Families of planar lattices with arbitrarily high $T_{\rm c}$ for the ferromagnetic Ising model
Periodic planar lattices are built via iterative triangulation to have arbitrarily high Ising critical temperatures, with Tc scaling as (2/ln2) ln q_max and Apollonian lattices conjectured optimal.
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Proof of entropic order in Generalized Ising Models
Rigorous proof establishes entropic order in generalized Ising models for p ≥ 1 and demonstrates they solve the NP-hard maximum independent set problem, leading to entropic glass phases.
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Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
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Entropic Barriers and the Kinetic Suppression of Topological Defects
Coupling to mesoscopic reservoirs generates temperature-increasing entropic barriers that suppress topological defect creation and transport, yielding three-regime correlation lengths in 1D Ising chains and double error reduction in finite-size 2D toric codes.