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We study the Ising model in a hierarchical small-world network by renormalization group analysis, and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges.…

Statistical Mechanics · Physics 2012-09-25 Tomoaki Nogawa , Takehisa Hasegawa , Koji Nemoto

We show that the canonical random-cluster measure associated to isoradial graphs is critical for all $q \geq 1$. Additionally, we prove that the phase transition of the model is of the same type on all isoradial graphs: continuous for $1…

Probability · Mathematics 2021-12-17 Hugo Duminil-Copin , Jhih-Huang Li , Ioan Manolescu

Quantum phase transition in the spin-boson model was claimed on the basis of various numerical studies, but not strictly proven. Here by using a unitary transformation to decompose the Hamiltonian into two branches of odd and even parity we…

Quantum Physics · Physics 2013-12-18 Tao Liu , Zexian Cao

We consider the Boolean model $Z$ on $\mathbb{R}^d$ with random compact grains, i.e. $Z := \bigcup_{i \in \mathbb{N}} (X_i + Z_i)$ where $\eta_t := \{X_1, X_2, \dots\}$ is a Poisson point process of intensity $t$ and $(Z_1, Z_2, \dots)$ is…

Probability · Mathematics 2016-07-22 Sebastian Ziesche

We establish the sharpness of the phase transition for a wide class of Gaussian percolation models, on $\mathbb{Z}^d$ or $\mathbb{R}^d$, $d \ge 2$, with correlations decaying at least algebraically with exponent $\alpha > 0$, including the…

Probability · Mathematics 2023-11-16 Stephen Muirhead

We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling study of the improved Blume-Capel model…

Statistical Mechanics · Physics 2012-05-21 Martin Hasenbusch

The phase-diagram of the two-dimensional Blume-Capel model with a random crystal field is investigated within the framework of a real-space renormalization group approximation. Our results suggest that, for any amount of randomness, the…

Statistical Mechanics · Physics 2009-10-30 N. S. Branco , Beatriz M. Boechat

A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-ohmic spin-Boson model. When the power s of the spectral function J(w) \propto w^s is smaller than 1/2, the…

Statistical Mechanics · Physics 2010-04-22 Andre Winter , Heiko Rieger , Matthias Vojta , Ralf Bulla

The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…

Discrete Mathematics · Computer Science 2022-05-10 Antonio Blanca , Alistair Sinclair

We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition (QPT) where the critical point exhibits an emergent enhanced symmetry. Such a transition…

Strongly Correlated Electrons · Physics 2025-08-27 Anirudha Menon , Anwesha Chattopadhyay , K. Sengupta , Arnab Sen

We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional…

Probability · Mathematics 2008-08-28 Massimo Campanino , Dmitry Ioffe , Yvan Velenik

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First we recover the known properties of the traditional model with…

Disordered Systems and Neural Networks · Physics 2025-03-25 Ferenc Iglói , Yu-Cheng Lin

We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective…

Disordered Systems and Neural Networks · Physics 2009-10-31 Thomas Nowotny , Heiko Patzlaff , Ulrich Behn

We prove that the correction to exponential decay of the truncated two points function in the homogeneous positive field Ising model is $c\|x\|^{-(d-1)/2}$. The proof is based on the development in the random current representation of a…

Mathematical Physics · Physics 2020-01-08 Sébastien Ott

The couplings between the Ising model and its graphical representations, the random-cluster, random current and loop $\mathrm{O}(1)$ models, are put on common footing through a generalization of the Swendsen-Wang-Edwards-Sokal coupling. A…

Probability · Mathematics 2025-06-13 Ulrik Thinggaard Hansen , Jianping Jiang , Frederik Ravn Klausen

With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the…

Statistical Mechanics · Physics 2023-06-21 Xiaohui Qian , Gaotian Yu , Nengji Zhou

Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots \times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that…

Probability · Mathematics 2019-01-11 Tom Hutchcroft

We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We discuss the possibility for such transitions…

By constructing an exactly solvable spin model, we investigate the critical behaviors of transverse field Ising chains interpolated with cluster interactions, which exhibit various types of topologically distinct Ising critical points.…

Strongly Correlated Electrons · Physics 2024-07-12 Xue-Jia Yu , Wei-Lin Li

Following seminal work by J. Fr\"ohlich and T. Spencer on the critical exponent $\alpha=2$, we give a proof via contours of phase transition in the one-dimensional long-range ferromagnetic Ising model in the entire region of decay, where…

Mathematical Physics · Physics 2024-12-31 Lucas Affonso , Rodrigo Bissacot , Henrique Corsini , Kelvyn Welsch