Publication

Phase Transition in Grand Canonical Φ23 Measure at Critical Chemical Potential

2026

Abstract

We study the phase transition and critical phenomenon for the grand canonical Φ3 measure in two-dimensional Euclidean quantum field theory. The study of this measure was initiated by Jaffe, Bourgain, and Carlen–Fröhlich–Lebowitz, primarily in regimes far from criticality. We identify a critical chemical potential and show that the measure exhibits a phase transition at this critical threshold. At the critical threshold, the analysis is based on establishing the correlation decay of the Gaussian fluctuations in the partition function, combined with a coarse-graining argument to show divergence of the maximum of an approximating Gaussian process.

Official source

https://infoscience.epfl.ch/entities/publication/96e96052-1110-4c04-ad04-ba447f948866

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/96e96052-1110-4c04-ad04-ba447f948866

About this result

Related concepts (31)

Partition function (quantum field theory)

In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism. They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Partition functions can rarely be solved for exactly, although free theories do admit such solutions. Instead, a perturbative approach is usually implemented, this being equivalent to summing over Feynman diagrams.

Critical phenomena

In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking.

Renormalization group

In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation.

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Phase Transition in Grand Canonical Φ23 Measure at Critical Chemical Potential

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