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Computing loop corrections by message passing.

A Ramezanpour¹

¹Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. abolfazl.ramezanpour@polito.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 16, 2013

Summary

This summary is machine-generated.

This study introduces a novel loop correction algorithm for the Ising model. The method uses spanning trees to accurately compute thermodynamic quantities and provides bounds for free energy.

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Area of Science:

Statistical mechanics
Computational physics
Graph theory

Background:

Loopy interaction graphs present challenges in computing thermodynamic quantities.
Exact mapping to tree graphs is possible via spanning trees.
Message-passing algorithms based on Bethe equations are commonly used.

Purpose of the Study:

To propose an approximation loop correction algorithm for the Ising model.
To address both short and long loops in interaction graphs.
To obtain upper and lower bounds for free energy.

Main Methods:

Utilizing spanning trees to represent loopy interaction graphs.
Mapping loopy graphs to extended tree graphs.
Applying a message-passing algorithm based on Bethe equations.
Developing an approximation loop correction algorithm.

Main Results:

The proposed algorithm effectively handles short and long loops simultaneously.
The method allows for the computation of thermodynamic quantities.
Upper and lower bounds for the free energy were obtained.

Conclusions:

The spanning tree representation provides an exact mapping for loopy graphs.
The approximation loop correction algorithm offers a robust method for the Ising model.
This approach enhances the calculation of free energy bounds in complex systems.