arXiv subjects

S. C. Park

Publications and source records attributed to S. C. Park.

9 recordsLinked to original sources

arXiv2026

Near-critical Ising, sine-Gordon at the free fermion point, and bosonization

In this article, we study the continuous correlations of the near-critical Ising model in two dimensions with plus boundary conditions, and prove that doubled correlation functions of primary fields (spin, disorder, fermions, energy) in the Ising model are given by correlation functions of the sine-Gordon model at the free fermion point. This is an instance of bosonization. The main ideas involve analyticity of correlation functions in a mass parameter in finite volume and proving that in a perturbative regime, the Taylor coefficients of the correlation functions match due to known bosonization results for the critical Ising model in terms of the Gaussian free field. The main techniques on the Ising side involve construction and precise estimates of certain massive holomorphic functions while on the sine-Gordon side, we control an iterated Mayer expansion with techniques going back to Brydges and Kennedy.

math-ph↗

arXiv2025

Conformal Invariance of the FK-Ising Model on Lorentz-Maximal S-Embeddings

We show on non-flat but critical s-embeddings the celebrated convergence of the interface curves of the critical FK Ising model to an $\operatorname{SLE}_{16/3}$ curve, using discrete complex analytic techniques first used in arXiv:0708.0039, arXiv:1312.0533 and subsequently extended to more lattice settings including isoradial graphs arXiv:0910.2045, circle packings arXiv:1712.08736, and flat s-embeddings arXiv:2006.14559. In our setting, the s-embedding approximates a maximal surface in the Minkowski space $\mathbb R^{2,1}$, an `exact' criticality condition identified in arXiv:2006.14559, which is stronger than the percolation-theoretic `near-critical' setup studied in, e.g., arXiv:2309.08470. The proof relies on a careful discretisation of the Laplace-Beltrami operator on the s-embedding, which is crucial in identifying the limit of the martingale observable.

math.PR↗

arXiv2022

On Isomonodromic Deformation of Massive Ising Spinors

In this short note, we give a self-contained derivation of the formula for the $2$-point full-plane Ising spin correlation function under massive scaling limit in terms of a third Painlevé transcendant. This formula, first derived in a celebrated work of Wu, McCoy, Tracy, and Barouch, was subsequently reformulated in terms of the theory of isomonodromic deformation by Sato, Miwa, and Jimbo. In view of recent developments in the discrete analysis which have enabled, in particular, a convergence proof of spin correlation functions on isoradial lattice, we give a concise and rigorous account of the continuous theory in the same framework yielding this iconic result.

math.PR↗

arXiv2022

Convergence of Fermionic Observables in the Massive Planar FK-Ising Model

We prove convergence of the 2- and 4-point fermionic observables of the FK-Ising model on simply connected domains discretised by a planar isoradial lattice in massive (near-critical) scaling limit. The former is alternatively known as a (fermionic) martingale observable (MO) for the massive interface, and in particular encapsulates boundary visit probabilties of the interface. The latter encodes connection probabilities in the 4-point alternating (generalised Dobrushin) boundary condition, whose exact convergence is then further analysed to yield crossing estimates for general boundary conditions. Notably, we obtain a massive version of the so-called Russo- Seymour-Welsh (RSW) type estimates on isoradial lattice. These observables satisfy a massive version of s-holomorphicity [Smi10], and we develop robust techniques to exploit this condition which do not require any regularity assumption of the domain or a particular direction of perturbation. Since many other near-critical observables satisfy the same relation (cf. [BeDu12, CIM21, Par19]), these strategies are of direct use in the analysis of massive models in broader setting.

math.PR↗

arXiv2021

Slit-strip Ising boundary conformal field theory 1: Discrete and continuous function spaces

This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of holomorphic functions in continuum domains as well as corresponding spaces of discrete holomorphic functions in lattice domains. We find distinguished sets of functions characterized by their singular behavior in the three infinite directions in the slit-strip domains. We prove convergence results of the distinguished discrete holomorphic functions to the continuum ones. In the subsequent articles, the discrete holomorphic functions will be used for the calculation of the Ising model fusion coefficients (as well as for the diagonalization of the Ising transfer matrix), and the convergence of the functions is used to prove the convergence of the fusion coefficients. It will also be shown that the vertex operator algebra of the boundary conformal field theory can be recovered from the limit of the fusion coefficients via geometric transformations involving the distinguished continuum functions.

math-ph↗

arXiv2021

Stellar Interferometry for Gravitational Waves

We propose a new method to detect gravitational waves, based on spatial coherence interferometry with stellar light, as opposed to the conventional temporal coherence interferometry with laser sources. The proposed method detects gravitational waves by using two coherent beams of light from a single distant star measured at separate space-based detectors with a long baseline. This method can be applied to either the amplitude or intensity interferometry. This experiment allows for the search of gravitational waves in the lower frequency range of $10^{-6}$ to $10^{-4}$ Hz. In this work, we present the detection sensitivity of the proposed stellar interferometer by taking the detector response and shot and acceleration noises into account. Furthermore, the proposed experimental setup is capable of searching for primordial black holes and studying the size of the target neutron star, which are also discussed in the paper.

astro-ph.HE↗

arXiv2021

Slit-strip Ising boundary conformal field theory 2: Scaling limits of fusion coefficients

This is the second in a series of three articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here we study the fusion coefficients of the Ising model in the lattice slit-strip, with locally monochromatic boundary conditions. The fusion coefficients are certain renormalized limits of boundary correlation functions at the three extremities of the truncated lattice slit-strips, in a basis of random variables whose correlation functions have an essentially exponential dependence on the truncation heights. The key technique is to associate operator valued discrete 1-forms to certain discrete holomorphic functions. This provides a direct analogy with currents in boundary conformal field theory. For two specific applications of this technique, we use distinguished discrete holomorphic functions from the first article of the series. First, we rederive the known diagonalization of the Ising transfer matrix in a form that parallels boundary conformal field theory. Second, we characterize the Ising model fusion coefficients by a recursion written purely in terms of inner products of the distinguished discrete holomorphic functions. The convergence result for the discrete holomorphic functions proven in the first part can then be used to derive the convergence of the fusion coefficients in the scaling limit. In the third article of the series, it will be shown that up to a transformation that accounts for our chosen slit-strip geometry, the scaling limits of the fusion coefficients become the structure constants of the vertex operator algebra of a fermionic conformal field theory.

math-ph↗

arXiv2019

Massive Scaling Limit of the Ising Model: Subcritical Analysis and Isomonodromy

We study the spin n-point functions of the planar Ising model on a simply connected domain Ωdiscretised by the square lattice δ\mathbb{Z}^{2} under near-critical scaling limit. While the scaling limit on the full-plane \mathbb{C} has been analysed in terms of a fermionic field theory, the limit in general Ωhas not been studied. We will show that, in a massive scaling limit wherein the inverse temperature is scaled β\simβ_{c}-m_{0}δfor a constant m_{0}<0, the renormalised spin correlations converge to a continuous quantity determined by a boundary value problem set in Ω. In the case of Ω=\mathbb{C} and n=2, this result reproduces the celebrated formula of [WMTB76] involving the Painlevé III transcendent. To this end, we generalise the comprehensive discrete complex analytic framework used in the critical setting to the massive setting, which results in a perturbation of the usual notions of analyticity and harmonicity.

math.PR↗

arXiv2018

Ising Model: Local Spin Correlations and Conformal Invariance

We study the 2-dimensional Ising model at critical temperature on a simply connected subset $Ω_δ$ of the square grid $δ\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by Conformal Field Theory; in particular, there is expected to be a precise correspondence between local lattice fields of the Ising model and the local fields of Conformal Field Theory. Towards the proof of this correspondence, we analyze arbitrary spin pattern probabilities (probabilities of finite spin configurations occurring at the origin), explicitly obtain their infinite-volume limits, and prove their conformal covariance at the first (non-trivial) order. We formulate these probabilities in terms of discrete fermionic observables, enabling the study of their scaling limits. This generalizes results of [Hon10,HoSm13] and [CHI15] to one-point functions of any local spin correlations. We introduce a collection of tools which allow one to exactly and explicitly translate any spin pattern probability (and hence any lattice local field correlation) in terms of discrete complex analysis quantities. The proof requires working with multipoint lattice spinors with monodromy (including construction of explicit formulae in the full plane), and refined analysis near their source points to prove convergence to the appropriate continuous conformally covariant functions.

math-ph↗