arXiv subjects

Paul Roux

Publications and source records attributed to Paul Roux.

5 recordsLinked to original sources

arXiv2026

Torus one-point functions in critical loop models

We show that in critical loop models, torus 1-point functions can be expressed in terms of sphere 4-point functions at a different central charge. Unlike in the Moore--Seiberg formalism, crossing symmetry on the sphere therefore implies modular covariance on the torus. We systematically compute torus 1-point functions in critical loop models, using a numerical bootstrap approach. We focus on the 1-point functions of the 6 simplest primary fields, which give rise to 10 solutions of modular covariance equations. Such 1-point functions are infinite linear combinations of conformal blocks. The coefficients are products of double Gamma functions, times polynomial functions of loop weights. For each solution, we determine the first 6 to 12 polynomials.

math-ph↗

arXiv2026

Exact solution of three-point functions in critical loop models

We propose an exact formula for three-point functions on the sphere in critical loop models with primary fields $V_{(r,s)}$ characterized by $2r$ legs and a parameter $s$ that describes diagonal fields for $r=0$ and the momentum of legs for $r>0$. We demonstrate its validity in three ways: the conformal bootstrap method for 4-point functions, a transfer-matrix study of the lattice model, and a probabilistic method based on conformal loop ensemble and Liouville quantum gravity. This work provides a crucial missing piece for solving critical loop models and reveals a deep unity between three fundamental approaches to 2D statistical physics: transfer matrix, conformal field theory, and probability theory.

cond-mat.stat-mech↗

arXiv2025

Three-point functions in critical loop models

In two-dimensional models of critical non-intersecting loops, there are $\ell$-leg fields that insert $\ell\in\mathbb{N}^*$ open loop segments, and diagonal fields that change the weights of closed loops. We conjecture an exact formula for 3-point functions of such fields on the sphere. In the cases of diagonal or spinless 2-leg fields, the conjecture agrees with known results from Conformal Loop Ensembles. We numerically compute 3-point functions in loop models on cylindrical lattices, using transfer matrix techniques. The results agree with the conjecture in almost all cases. We attribute the few discrepancies to difficulties that can arise in our lattice computation when the relevant modules of the unoriented Jones-Temperley--Lieb algebra have degenerate ground states.

math-ph↗

arXiv2024

Critical spin chains and loop models with $PSU(n)$ symmetry

Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the $O(n)$ model (symmetry group $O(n)$) and the Potts model (symmetry group $S_Q$). Both models make sense for $n,Q\in \mathbb{C}$ and not just $n,Q\in \mathbb{N}$, and both give rise to a conformal field theory in the critical limit. Here, we study similar models based on the group $PSU(n)$. We focus on the two-dimensional case, where the models can be described either as gases of non-intersecting orientable loops, or as alternating spin chains. This allows us to determine their spectra either by computing a twisted torus partition function, or by studying representations of the walled Brauer algebra. In the critical limit, our models give rise to a CFT that exists for any $n\in\mathbb{C}$ and has a global $PSU(n)$ symmetry. Its spectrum is similar to those of the $O(n)$ and Potts CFTs, but a bit simpler. We conjecture that the $O(n)$ CFT is a $\mathbb{Z}_2$ orbifold of the $PSU(n)$ CFT, where $\mathbb{Z}_2$ acts as complex conjugation.

hep-th↗

arXiv2022

Violent suicide attempt history in elderly patients with bipolar disorder: The role of sex, abdominal obesity, and verbal memory: Results from the FACE-BD cohort (FondaMental Advanced center of Expertise for Bipolar Disorders)

Background: Bipolar disorder (BD) is a chronic, lifelong condition, associated with increased risk of obesity, cognitive impairment, and suicidal behaviors. Abdominal obesity and a higher risk of violent suicide attempt (SA) seem to be shared correlates with older age, BD, and male sex until middle age when menopause-related female body changes occur. This study aimed at assessing the role of abdominal obesity and cognition in the violent SA burden of individuals with BD.Methods: From the well-defined nationwide cohort FACE-BD (FondaMental Advanced center of Expertise for Bipolar Disorders), we extracted data on 619 euthymic BD patients that were 50 years or older at inclusion. Cross-sectional clinical, cognitive, and metabolic assessments were performed. SA history was based on self-report.Results: Violent SA, in contrast to non-violent and no SA, was associated with higher waist circumference, abdominal obesity and poorer California Verbal Learning Test short-delay free recall (CVLT-SDFR) (ANOVA, p < .001, p = .014, and p = .006). Waist circumference and abdominal obesity were associated with violent SA history independently of sex, BD type and anxiety disorder (Exp(B) 1.02, CI 1.00-1.05, p = .018; Exp(B) 2.16, CI 1.00-4.64, p = .009, accordingly). In an exploratory model, waist circumference and CVLT-SDFR performance mediated the association between male sex and violent SA.Limitations: Cross-sectional design and retrospective reporting.Conclusions: Violent SA history was associated with abdominal obesity and poorer verbal memory in older age BD patients. These factors were interlinked and might mediate the association between male sex and violent SA.

q-bio.NC↗