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Updated: Apr 16, 2026
04:35
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
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Exact finite-size corrections for the spanning-tree model under different boundary conditions.
N Sh Izmailian1,2, R Kenna1
1Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom.
Summary
This study derives exact asymptotic expansions for spanning tree partition functions on square lattices under various boundary conditions. Results align with conformal field theory predictions, resolving discrepancies in free energy calculations.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Mathematical Physics
Background:
- Spanning trees on lattices are fundamental objects in statistical mechanics.
- Understanding their partition functions under different boundary conditions is crucial for theoretical advancements.
- Previous work has explored these models, but discrepancies with conformal field theory (CFT) predictions existed.
Purpose of the Study:
- To express spanning tree partition functions on finite square lattices under five boundary conditions.
- To derive exact asymptotic expansions for the logarithm of these partition functions.
- To reconcile apparent discrepancies between theoretical predictions and CFT for free energy calculations.
Main Methods:
- Expressing partition functions using a principal partition function with twisted boundary conditions.
- Deriving exact asymptotic expansions for the logarithm of the partition function.
- Establishing identities relating partition functions across different boundary conditions.
Main Results:
- Exact asymptotic expansions for spanning tree partition functions under five boundary conditions were derived.
- Identities connecting partition functions for different boundary conditions were established.
- Corner free energy for free-boundary conditions was found to agree with CFT predictions.
Conclusions:
- The study provides a unified framework for spanning tree partition functions on finite square lattices.
- The findings resolve discrepancies between lattice models and CFT predictions for free energy.
- The results offer valuable insights into the behavior of spanning trees in statistical physics.
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