PreprintCC BY 4.0arXiv
Locking transition in coupled disordered systems
Abstract
When a system of many interacting constituents is extended across space, every region carries the same disordered landscape, and it is unclear whether distant regions settle into the same state. We study copies of the Random Energy Model (REM), sharing one disorder realization, coupled along a chain. A first-order transition separates a phase with short-range correlations, from a locked phase in which the entire chain occupies the lowest-energy state with probability one, even at positive temperature. No intermediate ordering lengths occur. In the Generalized REM the chain locks either to the lowest-energy state or to the lowest free-energy valley.
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BibTeX
@misc{bunin2026locking,
title = {{Locking transition in coupled disordered systems}},
author = {Guy Bunin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36846},
eprint = {2609.36846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36846},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Locking transition in coupled disordered systems
AU - Guy Bunin
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36846
UR - https://arxiv.org/abs/2609.36846
AB - When a system of many interacting constituents is extended across space, every region carries the same disordered landscape, and it is unclear whether distant regions settle into the same state. We study copies of the Random Energy Model (REM), sharing one disorder realization, coupled along a chain. A first-order transition separates a phase with short-range correlations, from a locked phase in which the entire chain occupies the lowest-energy state with probability one, even at positive temperature. No intermediate ordering lengths occur. In the Generalized REM the chain locks either to the lowest-energy state or to the lowest free-energy valley.
ER -