We consider a $ϕ^4$-theory with a position-dependent distance from the critical point. One realization of this model is a classical ferromagnet subject to non-uniform mechanical stress. We find a sharp phase transition where the envelope of the local magnetization vanishes uniformly. The first-order transition in a quantum ferromagnet also remains sharp. The universal mechanism leading to a tricritical point in an itinerant quantum ferromagnet is suppressed, and in principle one can recover a quantum critical point with mean-field exponents. Observable consequences of these results are discussed.
The field-induced quantum criticality of compounds with ferromagnetically coupled structural spin units (as dimers and ladders) is explored by applying Wilson's renormalization group framework to an appropriate effective action. We determine the low-temperature phase boundary and the behavior of relevant quantities decreasing the temperature with the applied magnetic field fixed at its quantum critical point value. In this context, a plausible interpretation of some recent experimental results is also suggested.
In real magnets the tendency towards ferromagnetism, promoted by exchange coupling, is usually frustrated by dipolar interaction. As a result, the uniformly ordered phase is replaced by modulated (multi-domain) phases, characterized by different order parameters rather than the global magnetization. The transitions occurring within those modulated phases and towards the disordered phase are generally not of second-order type. Nevertheless, strong experimental evidence indicates that a standard critical behavior is recovered when comparatively small fields are applied that stabilize the uniform…
We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet by analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non trivial phase by commutativity breaking of the infinite volume limit and a suitable vanishing field. We find full agreement among theory, simulations and previous results.
Critical fluctuations change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, reduced anisotropy of nonlinear susceptibility acquires at $T_c$ the universal value $δ_4^* = {{2v^*} \over {3(u^* + v^*)}}$ where $u^*$ and $v^*$ -- coordinates of the cubic fixed point on the flow diagram of renormalization group equations. In the paper, the critical value of the reduced anisotropy is estimated within the pseudo-$ε$ expansion approach. The six-loop pseudo-$ε$ expansions…
We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We show that these systems are aging in the long-time regime, i.e., their two-time autocorrelation and response functions and associated fluctuation-dissipation ratio are non-trivial scaling functions of both time variables. This is exemplified by the exact analysis of the spherical model in any dimension D>2, and by numerical simulations on the two-dimensional Ising model. We show in particular that, for $1\ll s$ (waiting time) $\ll t$ (observation time), the fluctuation-dissipation…
An effective field theory is derived that describes the quantum critical behavior of itinerant ferromagnets as the transition is approached from the ferromagnetic phase. This complements a recent study of the critical behavior on the paramagnetic side of the phase transition, and investigates the role of the ferromagnetic Goldstone modes near criticality. We find that the Goldstone modes have no direct impact on the critical behavior, and that the critical exponents are the same as determined by combining results from the paramagnetic phase with scaling arguments.
We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a $\mathbb{Z}_3$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with $\mathbb{Z}_3\times\mathbb{Z}_3$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typica…
For the three-dimensional cubic model, the nonlinear susceptibilities of the fourth, sixth, and eighth orders are analyzed and the parameters δ^(i) characterizing their reduced anisotropy are evaluated at the cubic fixed point. In the course of this study, the renormalized sextic coupling constants entering the small-field equation of state are calculated in the four-loop approximation and the universal values of these couplings are estimated by means of the Pade-Borel-Leroy resummation of the series obtained. The anisotropy parameters are found to be: δ^(4) = 0.054 +/- 0.012, δ^(6) = 0.102 +/…
We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J1<0 (nearest-neighbor, ferromagnetic) and J2>0 (second-neighbor, antiferromagnetic) for g=J2/|J1|>1/2. Using Monte Carlo simulations and known analytical results, we demonstrate Ashkin-Teller criticality for g>= g*, i.e., the critical exponents vary continuously between those of the 4-state Potts model at g=g* and the Ising model for g -> infinity. Thus, stripe transitions offer a route to realizing a related class of conformal field theories with conformal charge c=1 …
Quantum critical systems out of equilibrium are of extensive interest, but are difficult to study theoretically. We consider here the steady state limit of a single electron transistor, which is attached to ferromagnetic leads and subjected to a finite bias voltage (V). In equilibrium (i.e., V=0), this system undergoes a continuous quantum phase transition with a critical destruction of the Kondo effect. We construct an exact quantum Boltzmann treatment in a dynamical large-N limit, and determine the universal scaling functions for the I-V characteristics covering both the linear and non-linea…
Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic $q$-state Potts model in $2+1d$. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of $q$, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be $ν=1$, saturating a modified version of the Harris-Luc…
The Grüneisen ratio (GR) has emerged as a superb tool for the diagnosis of quantum phase transitions, which diverges algebraically upon approaching critical points of continuous phase transitions. However, this paradigm has been challenged recently by observations of a finite GR for self-dual criticality and divergent GR at symmetry-enhanced first-order transitions. To unveil the fascinating GR further, we exemplify the idea by studying an exactly solvable quantum Ising model with Dzyaloshinskii-Moriya interaction, which harbors a ferromagnetic phase, a paramagnetic phase, and a chiral Lutting…
It is demonstrated that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse-square interactions exhibits a universal critical jump, in analogy with the superfluid density in helium films. Renormalization-group arguments are combined with numerical simulations of systems containing up to one million lattice sites to accurately determine the critical properties of these models. In strong contrast with earlier work, compelling quantitative evidence for the Kosterlitz--Thouless-like character of the phase transition is provided.
We discuss the effects of exponential fragmentation of the Hilbert space on phase transitions in the context of coupled ferromagnetic Ising models in arbitrary dimension with special emphasis on the one dimensional case. We show that the dynamics generated by quantum fluctuations is bounded within spatial partitions of the system and weak mixing of these partitions caused by global transverse fields leads to a zero temperature phase with ordering in the local product of both Ising copies but no long range order in either species. This leads to a natural connection with the Ashkin-Teller univer…
Guided by critical systems found in nature we develop a novel mechanism consisting of inhomogeneous polynomial regularisation via which we can induce scale invariance in deep learning systems. Technically, we map our deep learning (DL) setup to a genuine field theory, on which we act with the Renormalisation Group (RG) in momentum space and produce the flow equations of the couplings; those are translated to constraints and consequently interpreted as "critical regularisation" conditions in the optimiser; the resulting equations hence prove to be sufficient conditions for - and serve as an ele…
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the Mode-Coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by a geometric transition and large energy barriers, as expected from the lack of a…
We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantu…
The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both finite temperatures and disorder strength. We study the associated critical properties, by mapping the random 2D Ising model onto a network model. The model closely resembles network models of quantum Hall plateau transitions, but has different symmetries. Numerical transfer matrix calculations enable us to obtain estimates for the critical exponents at the rand…
We perform large-scale quantum Monte Carlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with $N=2$ spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength $U_c = 7.28 \pm 0.02$ in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding $N=2$ chiral Ising Gross-Neveu univer…
We consider 2D random Ising ferromagnetic models, where quenched disorder is represented either by random local magnetic fields (Random Field Ising Model) or by a random distribution of interaction couplings (Random Bond Ising Model). In both cases we first perform zero- and finite-temperature Monte-Carlo simulations to determine how the critical temperature depends on the disorder parameter. We then focus on the reversal transition triggered by an external field, and study the associated Barkhausen noise. Our main result is that the critical exponents characterizing the power-law associated w…
Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of tr…
We show that two-band superconductors harbor hidden criticality deep in the superconducting state, stemming from the critical temperature of the weaker band taken as an independent system. For sufficiently small interband coupling $γ$ the coherence length of the weaker band exhibits a remarkable deviation from the conventional monotonic increase with temperature, namely, a pronounced peak close to the hidden critical point. The magnitude of the peak scales proportionally to γ^(-μ), with the Landau critical exponent μ= 1/3, the same as found for the mean-field critical behavior with respect to …
We show that preferential rewiring, which is supposed to mimick the behaviour of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behaviour. For the non-rewired random graph version, due to a constant number of links out-going from each site, we write a simple mean-field-like equation describing the behaviour of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewirin…
We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a homogeneous critical external field. Our results extend earlier results by Rozikov and Ganikhodjaev.
Finite-temperature criticality through quantum annealing
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；RMIT University（皇家墨尔本理工大学）；Dipartimento di Fisica e Astronomia G. Galilei, Universitá degli Studi di Padova（帕多瓦大学伽利略物理与天文学系）；Dipartimento di Ingegneria dell’Informazione, Universitá degli Studi di Padova（帕多瓦大学信息工程系）；Padua Quantum Technologies Research Center, Università degli Studi di Padova（帕多瓦大学帕多瓦量子技术研究中心）；Weizmann institute of science（魏茨曼科学研究所）
We consider a finite sub-chain on an interval of the infinite XXX model in the ground state. The density matrix for such a subsystem was described in our previous works for the model with inhomogeneous spectral parameters. In the present paper, we give a compact formula for the physically interesting case of the homogeneous model.
