arXiv subjects

Pawat Akara-pipattana

Publications and source records attributed to Pawat Akara-pipattana.

8 recordsLinked to original sources

arXiv2026

Collective communication in a transparent world: Phase transitions in a many-body Potts model and a social--quantum correspondence

Digitally connected societies approach a ``transparent'' regime where all agents can interact without geographic or social barriers --- a limit realized by complete graph topologies. We construct a mean-field theory of a $q$-state Potts model with many-body interactions on this geometry, modeling agents from $q$ distinct communities. Analyzing the illustrative case of competing pairwise and three-body couplings, we identify three equilibrium phases in the thermodynamic limit: symmetric (all communities equal), reduced-symmetry ($q-1$ communities surviving), and consensus (one dominant group). For two-community systems, we identify a special coupling regime where the influence of interactions cancels out, yielding purely entropy-driven dynamics --- a statistical physics representation of atomized societies without structured influence. Monte Carlo simulations confirm these regimes and reveal metastable switching dynamics in finite systems. Furthermore, we establish a correspondence ($q \leftrightarrow N$) between this model and a mean-field $SU(N)$ quantum spin system with quadratic and cubic interactions. This ``social--quantum'' correspondence suggests a representation-theoretic description for classifying symmetry-broken macrostates and offers an interpretive link between quantum mean-field phase structure and opinion stratification.

physics.soc-ph↗

arXiv2026

Motif enrichment as a driver of scale-free behavior in rewired random regular graphs

We study the statistics of rewired random regular graphs (RRGs) in a mixed ensemble, where the average number of triangles is controlled by the fugacity $λ$, while the number of vertices and the vertex degree are fixed. This model exhibits a phase transition at critical fugacity $λ_{cr}$ from a triangle-poor phase (TPP), in which the number of triangles is independent of the system size, to a triangle-rich phase (TRP), in which the number of triangles scales linearly with the system size. We estimate $λ_{cr}$ by comparing the entropy of TPP with the energy of TRP. Above $λ_{cr}$, the RRG becomes a two-phase system in which dense clusters are connected by a sparse scale-free sub-network characterized by a degree distribution, $P(d) \sim d^{-γ}$, with $γ\approx 2$, independent of the size of the whole graph and its degree. We attribute this behavior to an "emergent preferential attachment" induced by triangle motifs, describe the mechanism underlying its formation, and derive the exponent $γ$ within a mean-field approach. We show that most inter-cluster triangles are isosceles, with the base lying inside one cluster and the apex belonging to the inter-cluster network. Finally, we speculate on a possible connection between these triangles and Efimov states in a conformally invariant potential.

cond-mat.dis-nn↗

arXiv2025

A set of master variables for the two-star random graph

The two-star random graph is the simplest exponential random graph model with nontrivial interactions between the graph edges. We propose a set of auxiliary variables that control the thermodynamic limit where the number of vertices N tends to infinity. Such `master variables' are usually highly desirable in treatments of `large N' statistical field theory problems. For the dense regime when a finite fraction of all possible edges are filled, this construction recovers the mean-field solution of Park and Newman, but with an explicit control over the 1/N corrections. We use this advantage to compute the first subleading correction to the Park-Newman result, which encodes the finite, nonextensive contribution to the free energy. For the sparse regime with a finite mean degree, we obtain a very compact derivation of the Annibale-Courtney solution, originally developed with the use of functional integrals, which is comfortably bypassed in our treatment.

cond-mat.stat-mech↗

arXiv2025

Statistical field theory of random graphs with prescribed degrees

Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of constraints that enforce the desired degree at each vertex. Building on top of recent results where similar methods are applied to random regular graph counting, we develop an accurate statistical field theory description for the adjacency matrix spectra of graphs with prescribed degrees. For large graphs, the expectation values are dominated by functional saddle points satisfying explicit equations. For the case of regular graphs, this immediately leads to the known McKay distribution. We then consider mixed-regular graphs with N1 vertices of degree d1, N2 vertices of degree d2, etc, such that the ratios N_i/N are kept fixed as N goes to infinity. For such graphs, the eigenvalue densities are governed by nonlinear integral equations of the Hammerstein type. Solving these equations numerically reproduces with an excellent accuracy the empirical eigenvalue distributions.

cond-mat.stat-mech↗

arXiv2025

Hammerstein equations for sparse random matrices

Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been previously applied to sparse matrix problems. We close this gap in the literature by showing how one can employ numerical solutions of Hammerstein equations to accurately recover the spectra of adjacency matrices and Laplacians of random graphs. While our treatment focuses on random graphs for concreteness, the methodology has broad applications to more general sparse random matrices.

cond-mat.dis-nn↗

arXiv2023

Random matrices with row constraints and eigenvalue distributions of graph Laplacians

Symmetric matrices with zero row sums occur in many theoretical settings and in real-life applications. When the offdiagonal elements of such matrices are i.i.d. random variables and the matrices are large, the eigenvalue distributions converge to a peculiar universal curve $p_{\mathrm{zrs}}(λ)$ that looks like a cross between the Wigner semicircle and a Gaussian distribution. An analytic theory for this curve, originally due to Fyodorov, can be developed using supersymmetry-based techniques. We extend these derivations to the case of sparse matrices, including the important case of graph Laplacians for large random graphs with $N$ vertices of mean degree $c$. In the regime $1\ll c\ll N$, the eigenvalue distribution of the ordinary graph Laplacian (diffusion with a fixed transition rate per edge) tends to a shifted and scaled version of $p_{\mathrm{zrs}}(λ)$, centered at $c$ with width $\sim\sqrt{c}$. At smaller $c$, this curve receives corrections in powers of $1/\sqrt{c}$ accurately captured by our theory. For the normalized graph Laplacian (diffusion with a fixed transition rate per vertex), the large $c$ limit is a shifted and scaled Wigner semicircle, again with corrections captured by our analysis.

cond-mat.dis-nn↗

arXiv2022

Resistance distance distribution in large sparse random graphs

We consider an Erdos-Renyi random graph consisting of N vertices connected by randomly and independently drawing an edge between every pair of them with probability c/N so that at N->infinity one obtains a graph of finite mean degree c. In this regime, we study the distribution of resistance distances between the vertices of this graph and develop an auxiliary field representation for this quantity in the spirit of statistical field theory. Using this representation, a saddle point evaluation of the resistance distance distribution is possible at N->infinity in terms of an 1/c expansion. The leading order of this expansion captures the results of numerical simulations very well down to rather small values of c; for example, it recovers the empirical distribution at c=4 or 6 with an overlap of around 90%. At large values of c, the distribution tends to a Gaussian of mean 2/c and standard deviation sqrt{2/c^3}. At small values of c, the distribution is skewed toward larger values, as captured by our saddle point analysis, and many fine features appear in addition to the main peak, including subleading peaks that can be traced back to resistance distances between vertices of specific low degrees and the rest of the graph. We develop a more refined saddle point scheme that extracts the corresponding degree-differentiated resistance distance distributions. We then use this approach to recover analytically the most apparent of the subleading peaks that originates from vertices of degree 1. Rather intuitively, this subleading peak turns out to be a copy of the main peak, shifted by one unit of resistance distance and scaled down by the probability for a vertex to have degree 1. We comment on a possible lack of smoothness in the true N->infinity distribution suggested by the numerics.

cond-mat.dis-nn↗

arXiv2021

The birth of geometry in exponential random graphs

Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex degree and form very large numbers of simple polygons (triangles or squares). The models avoid the collapse phenomena that plague naive graph Hamiltonians based on triangle or square counts. More than that, statistically significant numbers of other geometric primitives (small pieces of regular lattices, cubes) emerge in our ensemble, even though they are not in any way explicitly pre-programmed into the formulation of the graph Hamiltonian, which only depends on properties of paths of length 2. While much of our motivation comes from hopes to construct a graph-based theory of random geometry (Euclidean quantum gravity), our presentation is completely self-contained within the context of exponential random graph theory, and the range of potential applications is considerably more broad.

cond-mat.dis-nn↗