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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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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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.