arXiv subjects

Kay Joerg Wiese

Publications and source records attributed to Kay Joerg Wiese.

At least 19 recordsLinked to original sources

arXiv2026

Field theories for Laplacian Growth

Loop-erased random walks (LERW), the $O(n)$-model at ${n=-2}$ and Laplacian random walks (LRW) are three realizations of the same random process. While this equivalence holds on any graph, renormalization is possible only via the $O(-2)$-model. To generalize LRWs to $b$-LRWs or to Diffusion Limited Aggregation (DLA), a field theory directly on the Laplacian growth process is necessary. Here we construct an exact lattice action for LRWs and show that its perturbative expansion equals that of LERWs. We then generalize this approach to $b$-LRWs and DLA.

cond-mat.stat-mech↗

arXiv2026

Making complex CFTs real: The two-dimensional Potts model for $Q>4$ and complex $Q$

The two-dimensional $Q$-state Potts model with real couplings has a first-order transition for $Q>4$. Starting from a triangular-lattice Potts model with two- and three-spin interactions, we study an equivalent loop model in which $Q$ is a continuous parameter. By a combination of analytical and numerical arguments, we show that this loop model allows for the collision of a critical and a tricritical fixed point at $Q=4$. These then emerge as a pair of complex conformally invariant theories at $Q>4$, or even complex $Q$, for suitable complex coupling constants. We conjecture that all conformal data (such as the central charge, critical exponents, and three-point structure constants) can be obtained by analytic continuation of known exact results for the loop model with $Q \le 4$. This conjecture is checked, both for real $Q>4$ and for $Q \in \mathbb{C}$, by extensive transfer-matrix computations and comparison to previous studies for $Q=5$.

cond-mat.stat-mech↗

arXiv2026

Bayesian phase transition for the critical Ising model: Enlarged replica symmetry in the epsilon expansion and in 2D

A process that images or measures bond energies in the critical Ising model can be in distinct measurement ``phases'', depending on the precision of measurement. We study the transition into the strong-measurement phase using replica field theory (an epsilon expansion around six dimensions) and numerical simulations in two dimensions. The results reveal multiscaling of correlation functions at the critical point, and a striking enlarged symmetry of the replica description. This is an analog of the Nishimori phenomenon in the Ising spin glass, in a distinct replica limit. The enlarged symmetry is present microscopically for certain measurement protocols, but more generally can emerge in the infrared, and it fixes the exact value of the exponent for the Edwards-Anderson correlator both in 2D and near the upper critical dimension. We also examine the epsilon expansion for models with power-law interactions and/or long-range measurement.

cond-mat.stat-mech↗

arXiv2025

Roughness and critical force for depinning at 3-loop order

A $d$-dimensional elastic manifold at depinning is described by a renormalized field theory, based on the Functional Renormalization Group (FRG). Here we analyze this theory to 3-loop order, equivalent to third order in $ε=4-d$, where $d$ is the internal dimension. The critical exponent reads $ζ= \frac \epsilon3 + 0.04777 ε^2 -0.068354 ε^3 + {\cal O}(ε^4)$. Using that $ζ(d=0)=2^-$, we estimate $ζ(d=1)=1.266(20)$, $ζ(d=2)=0.752(1)$ and $ζ(d=3)=0.357(1)$. For Gaussian disorder, the pinning force per site is estimated as $f_{\rm c}= {\cal B} m^{2}ρ_m + f_{\rm c}^0$, where $m^2$ is the strength of the confining potential, $\cal B$ a universal amplitude, $ρ_m$ the correlation length of the disorder, and $f_{\rm c}^0$ a non-universal lattice dependent term. For charge-density waves, we find a mapping to the standard $ϕ^4$-theory with $O(n)$ symmetry in the limit of $n\to -2$. This gives $f_{\rm c} = \tilde {\cal A}(d) m^2 \ln (m) + f_{\rm c}^0 $, with $\tilde {\cal A}(d) = -\partial_n \big[ν(d,n)^{-1}+η(d,n)\big]_{n=-2}$, reminiscent of log-CFTs.

cond-mat.dis-nn↗

arXiv2025

Large Orders and Strong-Coupling Limit in Functional Renormalization

We study the large-order behavior of the functional renormalization group (FRG). For a model in dimension zero, we establish Borel-summability for a large class of microscopic couplings. Writing the derivatives of FRG as contour integrals, we express the Borel-transform as well as the original series as integrals. Taking the strong-coupling limit in this representation, we show that all short-ranged microscopic disorders flow to the same universal fixed point. Our results are relevant for FRG in disordered elastic systems.

hep-th↗

arXiv2025

Locating the Ising CFT via the ground-state energy on the fuzzy sphere

We locate the phase-transition line for the Ising model on the fuzzy sphere from a finite-size scaling analysis of its ground-state energy. Our strategy is to write the latter as $E_{GS}(N_m)/N_m = E_{0} + E_1 /N_m + E_{3/2}/N_m^{3/2}+ ...$, and to search for a minimum of $ χ:=E_{3/2}/E_0$ as a function of the couplings. Conformal perturbation theory predicts that around a CFT, $χ= χ_{\rm min} + \sum_i λ_i^2 N_m^{-ω_i} + O(λ^3)$, where $λ_i$ are the couplings associated to perturbations of operators with dimension $Δ_i$, and $ω_i = d-Δ_i$. This procedure finds the critical curve of [PRX 13 (2023) 021009] and their sweet spot with good precision. Varying two coupling constants allows us to extract the correction-to-scaling exponent $ω$ associated to the two leading scalars $ε$, and $ε'$. We find similar results when normalizing by the gap to the stress tensor $T$ or first parity-odd operator $σ$ instead of $E_0$.

hep-th↗

arXiv2024

Hyperuniformity in the Manna Model, Conserved Directed Percolation and Depinning

Hyperuniformity is an emergent property, whereby the structure factor of the density $n$ scales as $S(q) \sim q^α$, with $α>0$. We show that for the conserved directed percolation (CDP) class, to which the Manna model belongs, there is an exact mapping between the density $n$ in CDP, and the interface position $u$ at depinning, $n(x)=n_0+\nabla^2 u(x)$, where $n_0$ is the conserved particle density. As a consequence, the hyperuniformity exponent equals $α={4-d-2ζ}$, with $ζ$ the roughness exponent at depinning, and $d$ the dimension. In $d=1$, $α=1/2$, while $0.6> α\ge0$ for other $d$. Our results fit well simulations in the literature, except in $d=1$, where we perform our own to confirm this result. Such an exact relation between two seemingly different fields is surprising, and paves new paths to think about hyperuniformity and depinning. As corollaries, we get results of unprecedented precision in all dimensions, exact in $d=1$. This corrects earlier work on hyperuniformity in CDP.

cond-mat.stat-mech↗

arXiv2024

The two upper critical dimensions of the Ising and Potts models

We derive the exact actions of the $Q$-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless $Q$-component scalar field $Φ^α$. For the Ising model ($Q=2$), the field theory for the spins has upper critical dimension $d_{\rm c}^{\rm spin}=4$, whereas for the clusters it has $d_{\rm c}^{\rm cluster}=6$. As a consequence, the probability for three points to be in the same cluster is not given by mean-field theory for $d$ within $4<d<6$. We estimate the associated universal structure constant as $C=\sqrt{6-d}+ {\cal O}(6-d)^{3/2}$. This shows that some observables in the Ising model have an upper critical dimension of 4, while others have an upper critical dimension of $6$. Combining perturbative results from the $ε=6-d$ expansion with a non-perturbative treatment close to dimension $d=4$ allows us to locate the shape of the critical domain of the Potts model in the whole $(Q,d)$ plane.

hep-th↗

arXiv2024

Lattice realization of complex CFTs: Two-dimensional Potts model with $Q>4$ states

The two-dimensional $Q$-state Potts model with real couplings has a first-order transition for $Q>4$. We study a loop-model realization in which $Q$ is a continuous parameter. This model allows for the collision of a critical and a tricritical fixed point at $Q=4$, which then emerge as complex conformally invariant theories at $Q>4$, or even complex $Q$, for suitable complex coupling constants. All critical exponents can be obtained as analytic continuation of known exact results for $Q \le 4$. We verify this scenario in detail for $Q=5$ using transfer-matrix computations.

hep-th↗

arXiv2023

Depinning in the quenched Kardar-Parisi-Zhang class I: Mappings, simulations and algorithm

Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential energy may generate a different scaling behavior at depinning. The most experimentally relevant is the Kardar-Parisi-Zhang (KPZ) term, proportional to the square of the slope at each site, which drives the critical behavior into the so-called quenched KPZ (qKPZ) universality class. We study this universality class both numerically and analytically: by using exact mappings we show that at least for $d=1,2$ this class encompasses not only the qKPZ equation itself, but also anharmonic depinning and a well-known class of cellular automata introduced by Tang and Leschhorn. We develop scaling arguments for all critical exponents, including size and duration of avalanches. The scale is set by the confining potential strength $m^2$. This allows us to estimate numerically these exponents as well as the $m$-dependent effective force correlator $Δ(w)$, and its correlation length $ρ:= Δ(0)/|Δ'(0^+)|$. Finally we present a new algorithm to numerically estimate the effective ($m$-dependent) elasticity $c$, and the effective KPZ non-linearity $λ$. This allows us to define a dimensionless universal KPZ amplitude ${\cal A}:=ρλ/c$, which takes the value ${\cal A}=1.10(2)$ in all systems considered in $d=1$. This proves that qKPZ is the effective field theory for all these models. Our work paves the way for a deeper understanding of depinning in the qKPZ class, and in particular, for the construction of a field theory that we describe in a companion paper.

cond-mat.dis-nn↗

arXiv2023

Depinning in the quenched Kardar-Parisi-Zhang class II: Field theory

There are two main universality classes for depinning of elastic interfaces in disordered media: quenched Edwards-Wilkinson (qEW), and quenched Kardar-Parisi-Zhang (qKPZ). The first class is relevant as long as the elastic force between two neighboring sites on the interface is purely harmonic, and invariant under tilting. The second class applies when the elasticity is non-linear, or the surface grows preferentially in its normal direction. It encompasses fluid imbibition, the Tang-Leschorn cellular automaton of 1992 (TL92), depinning with anharmonic elasticity (aDep), and qKPZ. While the field theory is well developed for qEW, there is no consistent theory for qKPZ. The aim of this paper is to construct this field theory within the Functional renormalization group (FRG) framework, based on large-scale numerical simulations in dimensions $d=1$, $2$ and $3$, presented in a companion paper. In order to measure the effective force correlator and coupling constants, the driving force is derived from a confining potential with curvature $m^2$. We show, that contrary to common belief this is allowed in the presence of a KPZ term. The ensuing field theory becomes massive, and can no longer be Cole-Hopf transformed. In exchange, it possesses an IR attractive stable fixed point at a finite KPZ non-linearity $λ$. Since there is neither elasticity nor a KPZ term in dimension $d=0$, qEW and qKPZ merge there. As a result, the two universality classes are distinguished by terms linear in $d$. This allows us to build a consistent field theory in dimension $d=1$, which loses some of its predictive powers in higher dimensions.

cond-mat.dis-nn↗

arXiv2023

Experimental test of Sinai's model in DNA unzipping

The experimental measurement of correlation functions and critical exponents in disordered systems is key to testing renormalization group (RG) predictions. We mechanically unzip single DNA hairpins with optical tweezers, an experimental realization of the diffusive motion of a particle in a one-dimensional random force field, known as the Sinai model. We measure the unzipping forces $F_w$ as a function of the trap position $w$ in equilibrium and calculate the force-force correlator $Δ_m(w)$, its amplitude, and correlation length, finding agreement with theoretical predictions. We study the universal scaling properties since the effective trap stiffness $m^2$ decreases upon unzipping. Fluctuations of the position of the base pair at the unzipping junction $u$ scales as $u \sim m^{-ζ}$, with a roughness exponent $ ζ=1.34\pm0.06$, in agreement with the analytical prediction $ζ= \frac{4}{3}$. Our study provides a single-molecule test of the functional RG approach for disordered elastic systems in equilibrium.

cond-mat.dis-nn↗

arXiv2023

Renormalization group for measurement and entanglement phase transitions

We analyze the renormalization-group (RG) flows of two effective Lagrangians, one for measurement induced transitions of monitored quantum systems and one for entanglement transitions in random tensor networks. These Lagrangians, previously proposed on grounds of replica symmetry, are derived in a controlled regime for an illustrative family of tensor networks. They have different forms in the two cases, and involve distinct replica limits. The perturbative RG is controlled by working close to a critical dimensionality, ${d_c=6}$ for measurements and ${d_c=10}$ for random tensors, where interactions become marginal. The resulting RG flows are surprising in several ways. They indicate that in high dimensions $d>d_c$ there are at least two (stable) universality classes for each kind of transition, separated by a nontrivial tricritical point. In each case one of the two stable fixed points is Gaussian, while the other is nonperturbative. In lower dimensions, $d<d_c$, the flow always runs to the nonperturbative regime. This picture clarifies the "mean-field theory" of these problems, including the phase diagram of all-to-all quantum circuits. It suggests a way of reconciling exact results on tree tensor networks with field theory. Most surprisingly, the perturbation theory for the random tensor network (which also applies to a version of the measurement transition with "forced" measurements) formally possesses a dimensional reduction property analogous to that of the random-field Ising model. When only the leading interactions are retained, perturbative calculations in $d$ dimensions reduce to those in a simple scalar field theory in ${d-4}$ dimensions. We show that this holds to all orders by writing the action in a superspace formulation.

cond-mat.stat-mech↗

arXiv2023

Anchored advected interfaces, Oslo model, and roughness at depinning

There is a plethora of 1-dimensional advected systems with an absorbing boundary: the Toom model of anchored interfaces, the directed exclusion process where in addition to diffusion particles and holes can jump over their right neighbor, simple diffusion with advection, and Oslo sandpiles. All these models share a roughness exponent of $ζ=1/4$, while the dynamic exponent $z$ varies, depending on the observable. We show that for the first three models $z=1$, $z=2$, and $z=1/2$ are realized, depending on the observable. The Oslo model is apart with a conjectured dynamic exponent of $z=10/7$. Since the height in the latter is the gradient of the position of a disordered elastic string, this shows that $ζ=5/4$ for a driven elastic string at depinning.

cond-mat.dis-nn↗

arXiv2022

Force Correlations in Disordered Magnets

We present a proof of principle for the validity of the functional renormalization group, by measuring the force correlations in Barkhausen-noise experiments. Our samples are soft ferromagnets in two distinct universality classes, differing in the range of spin interactions, and the effects of eddy currents. We show that the force correlations have a universal form predicted by the functional renormalization group, distinct for short-range and long-range elasticity, and mostly independent of eddy currents. In all cases correlations grow linearly at small distances, as in mean-field models, but in contrast to the latter are bounded at large distances. As a consequence, avalanches are anti-correlated. We derive bounds for these anti-correlations, which are saturated in the experiments, showing that the multiple domain walls in our samples effectively behave as a single wall.

cond-mat.dis-nn↗

arXiv2022

Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles

Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modelled as an elastic system subject to quenched disorder. Its field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group flow involves a function, the disorder correlator $Δ(w)$, therefore termed the functional renormalization group (FRG). $Δ(w)$ is a physical observable, the auto-correlation function of the centre of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of these mappings requires specific techniques, which we develop, including modelling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbour interactions lead to directed percolation, and non-linear surface growth with additional KPZ terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random field magnets. Emphasis is given to numerical and experimental tests of the theory.

cond-mat.dis-nn↗

arXiv2022

Mean-Field Theories for Depinning and their Experimental Signatures

Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to model the latter: as a random walk (ABBM model), or as uncorrelated forces at integer $u$ (discretized particle model, DPM). While for many experiments ABBM (in the literature misleadingly equated with mean-field theory) makes quantitatively correct predictions, the microscopic disorder force-force correlations cannot grow linearly, and thus unboundedly as a random walk. Even the effective (renormalized) disorder forces which do so at small distances are bounded at large distances. We propose to model forces as an Ornstein Uhlenbeck process. The latter behaves as a random walk at small scales, and is uncorrelated at large ones. By connecting to results in both limits, we solve the model largely analytically, allowing us to describe in all regimes the distributions of velocity, avalanche size and duration. To establish experimental signatures of this transition, we study the response function, and the correlation function of position $u$, velocity $\dot u$ and forces $F$ under slow driving with velocity $v>0$. While at $v=0$ force or position correlations have a cusp at the origin, this cusp is rounded at a finite driving velocity. We give a detailed analytic analysis for this rounding by velocity, which allows us, given experimental data, to extract the time-scale of the response function, and to reconstruct the force-force correlator at $v=0$. The latter is the central object of the field theory, and as such contains detailed information about the universality class in question. We test our predictions by careful numerical simulations extending over up to ten orders in magnitude.

cond-mat.stat-mech↗

arXiv2020

Universal Force Correlations in an RNA-DNA Unzipping Experiment

We study unzipping of a complementary RNA-DNA helix applied to an external force, focusing on the force-force correlations. While at the microscopic level these are given by the sequence, the experiment measures effective, macroscopic correlations. The latter are sequence-independent, i.e. universal, and constitute the central object of the underlying field theory of disordered systems. Comparing field-theory predictions and the exact solution of a 1-d toy model with the experiment, we find an excellent agreement, confirming fundamental theoretical concepts via a biologically inspired experiments.

cond-mat.dis-nn↗