Abstract
We consider the Ising model at its critical temperature with external magnetic field ha15∕8 on aZ2. We give a purely probabilistic proof, using FK methods rather than reflection positivity, that for a=1, the correlation length is ≥const.h−8∕15 as h↓0. We extend to the a↓0 continuum limit the FK–Ising coupling for all h>0, and obtain tail estimates for the largest renormalized cluster area in a finite domain as well as an upper bound with exponent 1∕8 for the one-arm event. Finally, we show that for a=1, the average magnetization, M(h), in Z2 satisfies M(h)∕h1∕15→ some B∈(0,∞) as h↓0.
Original language | English (US) |
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Pages (from-to) | 560-583 |
Number of pages | 24 |
Journal | Stochastic Processes and their Applications |
Volume | 130 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2020 |
Keywords
- Correlation length
- Exponential decay
- FK-Ising coupling
- Ising model
- Magnetization exponent
- Magnetization field
- Near-critical
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics