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Title: Critical disorder and universality class of the MBL transition
Plain: If localization does occur above some disorder strength, the transition point and how quantities behave near it are unknown. Small-computer studies disagree with theories built on rare thermal patches.
Precise: Assuming $W_{c}$ exists for the random-field Heisenberg chain, determine $W_{c}/J$ and the scaling near the transition (Kosterlitz-Thouless-like versus a finite correlation-length exponent $\nu$, subject to the Harris-Chayes bound $\nu \ge 2$ in $d = 1$). Answer: $W_{c}$ with uncertainty and the scaling form of the characteristic length near $W_{c}$.
Settled by: Avalanche-stability numerics (chain coupled to an ideal bath at one end) extrapolated with a controlled scaling theory and consistent with renormalization-group predictions.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)