arXiv subjects

Toshiki Onagi

Publications and source records attributed to Toshiki Onagi.

4 recordsLinked to original sources

arXiv2026

A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions

The dipolar universality class describes the phase transition in 3D ferromagnets with strong dipolar interactions, as first discussed by Aharony and Fisher in the 1970s. While this universality class has been studied theoretically using renormalization group methods, as well as experimentally, little is known about it from Monte Carlo simulations. In this paper we aim to bridge this gap. We introduce a lattice model that faithfully implements the transverse constraint on the order parameter. We introduce a Markov Chain Monte Carlo algorithm which involves a combination of local Metropolis updates preserving the constraint, and a global update of the zero mode. We perform simulations on cubic lattices up to volume $48\times 48 \times 48$. We observe a continuous phase transition between the disordered and ordered phases. We obtain estimates of universal quantities such as the main critical exponents and the Binder ratio, and compare them with results from other techniques. We also investigate the emergence of rotation invariance at the critical point.

hep-th↗

arXiv2025

Transmission Coefficients from Phantom Currents

A representative quantity that characterizes the dynamics of conformal interfaces is the transmission coefficient, which is defined through correlation functions of the stress tensor. Typically, this coefficient is complicated and highly dependent on its details. In this work, we introduce a new perspective based on the notion of a ``phantom current''. We have shown that a spin-2 phantom current arising from the folding trick completely determines the transmission coefficient. In particular, when there is a single phantom current, the transmission coefficient is uniquely fixed by its conformal dimension. As a result, our framework provides a unified explanation of known results in minimal models and the free boson, while also yielding concrete predictions for previously unexplored interfaces.

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arXiv2025

Conformal Bootstrap with Duality-Inspired Fusion Rule

We present a systematic exploration of conformal field theories (CFTs) constrained by duality-inspired fusion rules using the conformal bootstrap. We classify the operator spectrum into three sectors: $[\sigma]$, $[\epsilon]$, and $[1]$. The $[\sigma]$ sector consists of all $\mathbb{Z}_{2}$-odd operators. The $\mathbb{Z}_{2}$-even operators are further divided into the $[\epsilon]$ sector, which contains only the operators that change sign under duality, and the $[1]$ sector, which encompasses all remaining operators. We impose a selection rule motivated by Kramers-Wannier duality, specifically forbidding the appearance of the $[\epsilon]$ sector in the $[\epsilon] \times [\epsilon]$ operator product expansion. By applying this constraint to the lowest-lying relevant scalars, we derive bounds on their conformal dimensions $(\Delta_\sigma, \Delta_\epsilon)$ in dimensions $d=2$ through $d=7$. Our bounds correctly allow the $d=2$ Ising model while excluding the $d=3$ Ising model, demonstrating the effectiveness of the imposed condition. Furthermore, we observe a distinct feature in $d=2$ corresponding to the $\mathcal{M}(8,7)$ minimal model and find non-trivial constraints in $d=3$ ($\Delta_\sigma \gtrsim 0.85$), relevant for theories like QED$_3$. This work opens a new avenue for non-perturbatively probing the landscape of CFTs constrained by fusion rules.

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arXiv2025

Monte Carlo study on Heisenberg model with local dipolar interaction

Aharony and Fisher showed that non-local dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point, called the dipolar fixed point. The non-perturbative nature of the new fixed point, however, has not been uncovered for many decades. Inspired by the recent understanding that the dipolar fixed point is scale-invariant but not conformal invariant, we perform the Monte Carlo simulation of the local Heisenberg-dipolar model on the lattice of $40^3$ by introducing the local cost function parameterized by a parameter $λ$ and study its critical exponents, which should become identical to the dipolar fixed point of Aharony and Fisher in the infinite coupling limit $λ= \infty$. We find that the critical exponents become noticeably different from those of the Heisenberg fixed point for a finite coupling constant $λ=8$ (e.g. $ν=0.601(2)(^{+0}_{-2})$ in the local Heisenberg-dipolar model while $ν=0.712(1)(^{+3}_{-0})$ in the Heisenberg model), and the spin correlation function has a feature that it becomes divergence-free, implying the lack of conformal invariance.

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