arXiv subjects

Kristian Blom

Publications and source records attributed to Kristian Blom.

10 recordsLinked to original sources

arXiv2026

Mean-Field Theory of Chiral Active Model B: Arrested Coarsening and Chiral Fingering Instabilities

We derive and analyze a mean-field theory of the chiral Ising model recently introduced by Wang, Pietzonka, and J\"ulicher in "Edge Currents Shape Condensates in Chiral Active Matter", arXiv:2603.20064. Starting from the master equation for clockwise and counterclockwise rotations of 2x2 spin blocks, we first obtain spatially discrete evolution equations for the spatially resolved average magnetization. On this discrete level, we show that a chiral bias strongly affects phase coarsening: domains coarsen anisotropically, develop nearly rectangular shapes, and eventually display chirality-induced arrested coarsening. Taking the continuum limit of these equations yields an active field theory that has the structure of a relaxational Model-B-type dynamics supplemented by a chiral current that permanently drives the system out of equilibrium. The coarse graining explicitly shows how microscopic rotational bias generates tangential currents localized at interfaces. Using this continuum theory, we perform a linear stability analysis of radially symmetric clusters and identify a chiral fingering instability in which angular perturbations of the interface are amplified and eventually lead to radially asymmetric rotating states or disordered states.

nlin.PS↗

arXiv2026

Strong Mpemba Effect Through a Reentrant Phase Transition

We investigate temperature quenches across the reentrant phase transition of the antiferromagnetic Ising model in a magnetic field and show that it provides a natural mechanism for strong direct and inverse Mpemba effects. For quenches terminating in the paramagnetic phase, the slowest relaxation mode is purely staggered. Initial states in the paramagnetic phase therefore have exactly zero overlap with this mode and exhibit a strong Mpemba effect, whereas antiferromagnetic initial states excite it and develop a slow-relaxation tail. Moreover, reentrance makes the equilibrium staggered magnetization nonmonotonic, producing conventional direct and inverse Mpemba effects when both initial states lie in the antiferromagnetic phase and the quench terminates in the paramagnetic phase. By varying the lattice coordination number, we show that this mechanism disappears in the absence of reentrance. Our results provide the first demonstration of (strong) Mpemba effects in the antiferromagnetic Ising model within the pair approximation and establish a direct link between anomalous relaxation and equilibrium phase behavior.

cond-mat.stat-mech↗

arXiv2025

Dynamic Models for Two Nonreciprocally Coupled Fields: A Microscopic Derivation for Zero, One, and Two Conservation Laws

We construct dynamic models governing two nonreciprocally coupled fields for several cases with zero, one, and two conservation laws. Starting from two microscopic nonreciprocally coupled Ising models, and using the mean-field approximation, we obtain closed-form evolution equations for the spatially resolved magnetization in each lattice. Only allowing for single spin-flip dynamics, the macroscopic equations in the thermodynamic limit are closely related to the nonreciprocal Allen-Cahn equations, i.e. conservation laws are absent. Likewise, only accounting for spin-exchange dynamics within each lattice, the thermodynamic limit yields equations similar to the nonreciprocal Cahn-Hilliard model, i.e. with two conservation laws. In the case of spin-exchange dynamics within and between the two lattices, we obtain two nonreciprocally coupled equations that add up to one conservation law. For each of these cases, we systematically map out the linear instabilities that can arise. Moreover, combining the different dynamics gives a large number of further models. Our results provide a microscopic foundation for a broad class of nonreciprocal field theories, establishing a direct link between nonequilibrium statistical mechanics and macroscopic continuum descriptions.

cond-mat.stat-mech↗

arXiv2024

Hallmarks of Deception in Asset-Exchange Models

We investigate the transient and steady-state dynamics of the Bennati-Dragulescu-Yakovenko money game in the presence of probabilistic cheaters, who can misrepresent their financial status by claiming to have no money. We derive the steady-state wealth distribution per player analytically, and show how the presence of hidden cheaters can be inferred from the relative variance of wealth per player. In scenarios with a finite number of cheaters amidst an infinite pool of honest players, we identify a critical probability of cheating at which the total wealth owned by the cheaters experiences a second-order discontinuity. Below this point, the transition probability to lose money is larger than the probability to gain; conversely, above this point, the direction is reversed. We further establish a threshold cheating probability at which cheaters collectively possess half of the total wealth in the game. Lastly, we provide bounds on the rate at which both cheaters and honest players can gain or lose wealth, contributing to a deeper understanding of deception in asset exchange models.

cond-mat.stat-mech↗

arXiv2024

Local Order Controls the Onset of Oscillations in the Nonreciprocal Ising Model

We elucidate the generic bifurcation behavior of local and global order in the nonreciprocal Ising model evolving under Glauber dynamics. We show that a critical magnitude of nearest-neighbor correlations within the respective lattices controls the emergence of coherent oscillations of global order as a result of frustration. Local order is maintained during these oscillations, implying nontrivial spatiotemporal correlations. Long-lived states emerge in the strong-interaction regime. The residence time in either of these states eventually diverges, giving rise to ordered non-equilibrium trapped states and a loss of ergodic behavior via a saddle-node-infinite-period bifurcation. Our work provides a comprehensive microscopic understanding of the nonreciprocal Ising model beyond the mean-field approximation.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium statistical mechanics of money/energy exchange models

Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations - a proof of the exponential steady-state distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model, and its extensions, using a simple mean-field-type approach that examines the properties of the one-dimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steady-state distribution in this model. Breaking the time-reversal symmetry of the game by modifying its rules results in non-Boltzmann steady-state statistics. In particular, introducing "unfair" exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Pareto-type power-law distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the "ground state" (i.e., with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant's wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game.

cond-mat.stat-mech↗

arXiv2023

Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss

Many non-equilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may -- via a process called milestoning -- improve entropy-production estimates. Milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory. Moreover, whereas the correct general physical definition of time-reversal in the presence of memory remains unknown, we here show by means of systematic, physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time-reversal generally must be discarded.

cond-mat.stat-mech↗

arXiv2023

Global Speed Limit for Finite-Time Dynamical Phase Transition and Nonequilibrium Relaxation

Recent works unraveled an intriguing finite-time dynamical phase transition in the thermal relaxation of the mean field Curie-Weiss model. The phase transition reflects a sudden switch in the dynamics. Its existence in systems with a finite range of interaction, however, remained unclear. Here we demonstrate the dynamical phase transition for nearest-neighbor Ising systems on the square and Bethe lattices through extensive computer simulations and by analytical results. Combining large-deviation techniques and Bethe-Guggenheim theory we prove the existence of the dynamical phase transition for arbitrary quenches, including those within the two-phase region. Strikingly, for any given initial condition we prove and explain the existence of non-trivial speed limits for the dynamical phase transition and the relaxation of magnetization, which are fully corroborated by simulations of the microscopic Ising model but are absent in the mean field setting. Pair correlations, which are neglected in mean field theory and trivial in the Curie-Weiss model, account for kinetic constraints due to frustrated local configurations that give rise to a global speed limit.

cond-mat.stat-mech↗

arXiv2023

Thermodynamically Consistent Phase-Field Theory Including Nearest-Neighbor Pair Correlations Explains Failure of Mean-Field Reasoning

Most of our current understanding of phase separation is based on ideas that disregard correlaions. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which are decisive in systems with strong interactions. Evaluating the continuum limit of the Ising model on the Bethe-Guggenheim level, we derive a Cahn-Hilliard free energy that takes into account pair correlations. For a one-dimensional interface in a strip geometry these are shown to give rise to an effective interface broadening at interaction strengths near and above the thermal energy, which is verified in the Ising model. Interface broadening is the result of an entropy-driven interface delocalization, which is not accounted for in the widely adopted mean field theory. Pair correlations are required for thermodynamic consistency as they enforce a thermodynamically optimal local configuration of defects and profoundly affect nucleation and spinodal decomposition at strong coupling.

cond-mat.stat-mech↗

arXiv2021

Criticality in Cell Adhesion

We illuminate the many-body effects underlying the structure, formation, and dissolution of cellular adhesion domains in the presence and absence of forces. We consider mixed Glauber-Kawasaki dynamics of a two-dimensional model of nearest-neighbor interacting adhesion bonds with intrinsic binding-affinity under the action of a shared pulling or pushing force. We consider adhesion bonds that are immobile due to being anchored to the underlying cytoskeleton as well as adhesion molecules that are transiently diffusing. Highly accurate analytical results are obtained on the pair-correlation level of the Bethe-Guggenheim approximation for the complete thermodynamics and kinetics of adhesion clusters of any size, including the thermodynamic limit. A new kind of dynamical phase transition is uncovered -- the mean formation and dissolution times per adhesion bond change discontinuously with respect to the bond-coupling parameter. At the respective critical points cluster formation and dissolution are fastest, while the statistically dominant transition path undergoes a qualitative change -- the entropic barrier to complete binding/unbinding is rate-limiting below, and the phase transition between dense and dilute phases above the dynamical critical point. In the context of the Ising model the dynamical phase transition reflects a first-order discontinuity in the magnetization-reversal time. Our results provide a potential explanation for the mechanical regulation of cell adhesion, and suggest that the quasi-static and kinetic response to changes in the membrane stiffness or applied forces is largest near the statical and dynamical critical point, respectively.

cond-mat.stat-mech↗