Field theory for zero temperature soft anharmonic spin glasses in a field

Urbani, Pierfrancesco

doi:10.1088/1751-8121/ac8088

Cited by 4 publications

(2 citation statements)

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“…Finally, it would be interesting to develop an analysis of the Hessian of harmonic fluctuation at zero temperature as in [49]. Here the analysis could be carried on by using the technique as developed in [50]. We can foresee that the result of this analysis in the solid phase will give rise to a gapless density of states following D(ω) ∼ ω ν law with ν = 2.…”

Section: Discussionmentioning

confidence: 99%

A continuous constraint satisfaction problem for the rigidity transition in confluent tissues

Urbani¹

2023

J. Phys. A: Math. Theor.

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Models of confluent tissues are built out of tessellations of the space (both in two and three dimensions) in which the cost function is constructed in such a way that individual cells try to optimize their volume and surface in order to reach a target shape. At zero temperature, many of these models exhibit a rigidity transition that separates two phases: a liquid phase and a solid (glassy) phase. This phenomenology is now well established but the theoretical understanding is still not complete. In this work we consider an exactly soluble mean field model for the rigidity transition which is based on an abstract mapping. We replace volume and surface functions by random non-linear functions of a large number of degrees of freedom forced to be on a compact phase space. We then seek for a configuration of the degrees of freedom such that these random non-linear functions all attain the same value. This target value is a control parameter and plays the role of the target cell shape in biological tissue models. Therefore we map the microscopic models of cells to a random continuous constraint satisfaction problem with equality constraints. We argue that at zero temperature, the rigidity transition corresponds to the satisfiability transition of the problem. We also characterize both the satisfiable (SAT) and unsatisfiable (UNSAT) phase. In the SAT phase, before reaching the rigidity transition, the zero temperature SAT landscape undergoes an replica symmetry breaking (RSB)/ergodicity breaking transition of the same type as the Gardner transition in amorphous solids. By solving the RSB equations we compute the SAT/UNSAT threshold and the critical behavior around it. In the UNSAT phase we also compute the average shape index as a function of the target one and we compare the thermodynamical solution of the model with the results of the numerical greedy minimization of the corresponding cost function.

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Section: Discussionmentioning

confidence: 99%

A continuous constraint satisfaction problem for the rigidity transition in confluent tissues

Urbani¹

2023

J. Phys. A: Math. Theor.

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“…Unfortunately, our present method does not work for general values of h i 's. We restrict our analysis for a specific case [29]:…”

Section: Modelmentioning

confidence: 99%

Bose–Einstein-like condensation of deformed random matrix: a replica approach

Ikeda¹

2023

J. Stat. Mech.

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In this work, we investigate a symmetric deformed random matrix, which is obtained by perturbing the diagonal elements of the Wigner matrix. The eigenvector x m i n of the minimal eigenvalue λ m i n of the deformed random matrix tends to condensate at a single site. In certain types of perturbations and in the limit of the large components, this condensation becomes a sharp phase transition, the mechanism of which can be identified with the Bose–Einstein condensation in a mathematical level. We study this Bose–Einstein like condensation phenomenon by means of the replica method. We first derive a formula to calculate the minimal eigenvalue and the statistical properties of x m i n . Then, we apply the formula for two solvable cases: when the distribution of the perturbation has the double peak, and when it has a continuous distribution. For the double peak, we find that at the transition point, the participation ratio changes discontinuously from a finite value to zero. On the contrary, in the case of a continuous distribution, the participation ratio goes to zero either continuously or discontinuously, depending on the distribution.

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