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This research aims to establish the occurrence of phase transitions in the long-range random field Ising model within lower dimensions.

Phase transition of the long range Ising model in lower dimensions, for d < α ≤ d + 1, with a Peierls argument

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This research aims to establish the occurrence of phase transitions in the long-range random field Ising model within lower dimensions.
Extends earlier findings by employing a novel Peierls argument to analyze lower dimensional phase transitions.
Utilizes combinatorial enumeration to investigate suitable paths within contour systems.
Applies a coarse-graining approach analogous to Renormalization group techniques in Statistical Physics.
Demonstrated a distinct phase transition occurs for the random field Ising model in lower dimensions.
Characterized lower-dimensional contours exhibiting different behaviors under boundary conditions compared to higher dimensions.
Introduced a new flipping procedure for spins that plays a critical role in evaluating interactions and configurations.

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Randomized analysis demonstrates phase transition in lower-dimensional Ising models, suggesting innovative insights into spin behavior.

Pete Rigas (2026) studied this question.

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