arXiv subjects

Kari Rummukainen

Publications and source records attributed to Kari Rummukainen.

At least 19 recordsLinked to original sources

arXiv2026

Seeded bubble nucleation on the lattice

We provide the first non-perturbative lattice determination of the bubble nucleation rate as seeded by topological defects during a first order phase transition. Our case of study is the cubic anisotropy model, which can mimic the Higgs-plus-singlet setup for the electroweak theory, in $d=2+1$ spacetime dimensions, where bubbles are seeded by (line-like) domain walls. We compare the nucleation rate from the lattice with the semi-classical prediction based on the effective field theory living on the domain walls, including for the first time the fluctuation determinant away from spherical symmetry. Our results show very good agreement across all the considered parameter space.

hep-lat↗

arXiv2026

Lattice study of the critical bubble in $\mathrm{SU(8)}$ deconfinement transition

Strongly coupled theories are of phenomenological interest, for example as dark matter candidates. Theories that can undergo first order thermal phase transitions are particularly appealing as potential sources of a stochastic gravitational wave background. Determining the expected gravitational wave signal from a first order phase transition requires accurate information on the bubble nucleation rate, but thus far for strongly coupled models these have relied on semiclassical methods. As a first step towards determining the nucleation rate, in this paper we study the confinement-deconfinement phase transition in a 4D SU(8) pure gauge model, using multicanonical Monte Carlo. Resolving the critical bubble for the first time in a pure Yang-Mills model, we determine the critical bubble probability and compare it to results from thin wall calculations. We also compare the effectiveness of different lattice pseudo-order parameters at resolving the condensation transition between the metastable phase and critical bubble branch, and point out the choice of order parameter is crucial to accurately resolve the critical configurations.

hep-lat↗

arXiv2025

The spectrum of axions in a scaling string network

Cosmic strings formed when the Peccei-Quinn symmetry breaks post-inflation are expected to emit axions throughout their lifetime. The details of the evolution of this network and the associated spectrum of axions are crucial for obtaining an accurate axion mass prediction, thus guiding searches at haloscopes. In a previous publication, we obtained evidence for the standard scaling of axion string networks, showing that the number of horizon lengths of string per horizon volume asymptotes to an $\mathcal{O}(1)$ constant. In this article, we turn our attention to the axion spectra, studying spectra of all components of the axion current and their unequal time correlators. With the new information we are better able to distinguish the contributions from propagating axions from the field carried by the strings, and show that previous measurements of the axion energy spectrum based only on the timelike component of the current are approximately 30\% derived from the string fields. We introduce a simple model based on an ensemble of string segments, which accounts for the general features of the spectra and time correlations. We conclude that axion emission from a scaling string network is close to scale-invariant ($q \approx 1$), and that the energy spectrum of sub-horizon modes behaves as $p_\text{ax}\ln( k \tau)$, where $k$ is the comoving wavenumber, $\tau$ the conformal time and $p_\text{ax} \simeq 10$. The number density spectrum evolves towards a single curve for $k\tau \lesssim 10^2$, with higher wavenumber deviations arising from initial conditions and resonant axion production at the string width scale. The total number density of axions produced from strings is $n_\text{ax}=1.66(17) f_\text{a}^2 H$, where $f_\text{a}$ is the axion decay constant and $H$ the Hubble rate. We report on axion production from the final collapse of the network in a future work.

hep-ph↗

arXiv2025

Confined-deconfined interface tension and latent heat in SU(N) gauge theory

We present high-precision lattice results for the confined-deconfined interface tension and the latent heat of pure SU($N$) gauge theories up to $N=10$ and investigate their asymptotic $N$-dependency. For both quantities we observe the leading $N^2$ behaviour and subleading corrections, with the result for the interface tension $\sigma/T_c^3 = 0.0182(7) N^2 - 0.194(15)$ and for the latent heat $L/T_c^4 = 0.360(6) N^2 - 1.88(17)$. We use the \emph{mixed phase ensemble} method - where the system is constrained so that half of the volume is in the confined phase and the other half in the deconfined phase - and the interface tension is obtained by measuring the capillary wave fluctuation spectra of the interfaces between the two phases. The method bypasses supercritical slowing down from which other methods for determining the interface tension suffer, and as a by-product produces accurate estimates of the critical inverse gauge coupling as a function of the inverse temperature. We use the latter to determine the lattice beta function values, required to compute the latent heat from the discontinuity in the average plaquette action across the confined-deconfined transition.

hep-lat↗

arXiv2025

Non-perturbative determination of the sphaleron rate for first-order phase transitions

In many extensions of the Standard Model electroweak phase transitions at high temperatures can be described in a minimal dimensionally reduced effective theory with SU(2) gauge field and fundamental Higgs scalar. In this effective theory, all thermodynamic information is governed by two dimensionless ratios $x \equiv \lambda_3/g^2_3$ and $y\equiv m^2_3/g^4_3$, where $\lambda_3$, $m^2_3$ and $g_3$ are the effective thermal scalar self-interaction coupling, the thermal mass and the effective gauge-coupling, respectively. By using non-perturbative lattice simulations to determine the rate of sphaleron transitions in the entire $(x,y)$-plane corresponding to the Higgs phase, and by applying previous lattice results for the bubble nucleation, we find a condition $x(T_c) \lesssim 0.025$ to guarantee preservation of the baryon asymmetry, which translates to $v/T_c \equiv \sqrt{2 \Delta \langle \phi^\dagger \phi \rangle}/T_c \gtrsim 1.33$ for the (gauge-invariant) discontinuity in Higgs condensate. This indicates that viability of the electroweak baryogenesis requires the phase transition to be slightly stronger than previously anticipated. Finally, we present a general template for analysing such viability in a wide class of beyond the Standard Model theories, in which new fields are heavy enough to be integrated out at high temperature.

hep-ph↗

arXiv2025

Gravitational waves from strong first order phase transitions

We study gravitational wave production at strong first order phase transitions, with large-scale, long-running simulations of a system with a scalar order parameter and a relativistic fluid. One transition proceeds by detonations with asymptotic wall speed $v_\text{w}=0.92$ and transition strength $\alpha_n=0.67$, and the other by deflagrations, with a nominal asymptotic wall speed $v_\text{w}=0.44$ and transition strength $\alpha_n=0.5$. We investigate in detail the power spectra of velocity and shear stress and - for the first time in a phase transition simulation - their time decorrelation, which is essential for the understanding of gravitational wave production. In the detonation, the decorrelation speed is larger than the sound speed over a wide range of wavenumbers in the inertial range, supporting a visual impression of a flow dominated by supersonic shocks. Vortical modes do not contribute greatly to the produced gravitational wave power spectra even in the deflagration, where they dominate over a range of wavenumbers. In both cases, we observe dissipation of kinetic energy by acoustic turbulence, and in the case of the detonation an accompanying growth in the integral scale of the flow. The gravitational wave power approaches a constant with a power law in time, from which can be derived a gravitational wave production efficiency. For both cases this is approximately $\tilde{\Omega}^\infty_\text{gw} \simeq 0.017$, even though they have quite different kinetic energy densities. The corresponding fractional density in gravitational radiation today, normalised by the square of the mean bubble spacing in Hubble units, for flows which decay in much less than a Hubble time, is $\Omega_{\text{gw},0}/(H_\text{n} R_*)^2=(4.8\pm1.1)\times 10^{-8}$ for the detonation, and $\Omega_{\text{gw},0}/(H_\text{n} R_*)^2=(1.3\pm0.2)\times 10^{-8}$ for the deflagration.

astro-ph.CO↗

arXiv2025

Expanded ensemble method for bubble nucleation

In the absence of impurities and boundary effects, first order phase transitions are initiated by the nucleation of critical bubbles. In thermally driven transitions many systems can remain metastable for an extended time, possibly tens of orders of magnitude longer than typical microscopic timescales. In standard Markov chain Monte Carlo simulations of these systems the probability of critical bubbles can be too suppressed for the transition to happen in any practical simulation time. The computation can be accelerated by using modified sampling methods, for example multicanonical or Wang-Landau sampling. However, even using these methods, there remains a condensation barrier which dramatically reduces the efficiency at large volumes. We present a novel sampling method, the method of expanded ensembles, which very effectively circumvents the condensation barrier and enables efficient simulations at large volumes.

hep-lat↗

arXiv2025

The confined-deconfined surface tension in SU(N) gauge theories at large N

We present results from an investigation of the $N$-dependency of the confined-deconfined interface tension and latent heat in pure SU($N$) gauge theory at large $N$. The interface tension is determined by measuring the transverse fluctuations of the phase interface on large lattices with coexisting confined and deconfined phases. We observe unambiguously that both the interface tension and latent heat scale as $N^2$ at large $N$.

hep-lat↗

arXiv2025

Resolving the critical bubble in SU(8) deconfinement transition

Strongly coupled confining models with a first order phase transition present an interesting DM candidate. Near the critical temperature these models are strongly non-perturbative, and the critical bubble nucleation rate has so far only been estimated via approximative methods. As a model of a strong first order deconfinement transition, we simulate 4D SU(8) pure gauge model with multicanonical Monte Carlo. We demonstrate that resolving the critical bubble is possible in a strongly coupled model. We calculate the free energy of a critical bubble, which gives a rough upper limit for the nucleation rate. For the parameter points we investigated, the thin-wall approximation for the critial bubble free energy is off by a factor of 2, overestimating the rate at least by a factor of $e^{10}$.

hep-lat↗

arXiv2024

Scaling density of axion strings in terasite simulations

We report on a study of axion string networks using fixed-grid simulations of up to $16384$ points per side. The length of string can be characterised in terms of standard dimensionless parameters $\zeta_\text{w}$ and $\zeta_\text{r}$, the length density measured in the cosmic rest frame and the string rest frame, scaled with the cosmic time. The motion of the string can be characterised by the root-mean-square (RMS) velocity of the string. Starting from a range of initial length densities and velocities, we analyse the string network in the standard scaling framework and find evolution towards a fixed point with estimated values $\hat{\zeta}_{\text{w},*} = 1.220(57)$ and $\hat{\zeta}_{\text{r},*} = 1.491(93)$. The two measures are related by the RMS velocity, which we estimate to be $\hat{v}_{*} = 0.5705(93)$. The length density is consistent with previous measurements, while the velocity is about 5% lower. For simulations starting from low enough density, the length density parameters $\zeta_\text{w}$ and $\zeta_\text{r}$ remain below their fixed point values throughout, while growing slowly, giving rise to an impression of approximately logarithmic increase with time. This has been proposed as the true long-term behaviour. We find that the growth tends to slow down as the values of $\zeta_\text{w}$ and $\zeta_\text{r}$ identified as fixed points are approached. In the case of $\zeta_\text{r}$, the growth stops for simulations which started close to the fixed point length density. The difference between $\zeta_\text{w}$ and $\zeta_\text{r}$ can be understood to result from the continuing velocity evolution. Our results indicate that the growth of $\zeta_\text{w}$ is a transient appearing at low densities and while the velocity is converging. This highlights the importance of studying the string density and the velocity together, and the preparation of initial conditions.

hep-ph↗

arXiv2024

Primordial acoustic turbulence: three-dimensional simulations and gravitational wave predictions

Gravitational waves (GWs) generated by a first-order phase transition at the electroweak scale are detectable by future space-based detectors like LISA. The lifetime of the resulting shock waves plays an important role in determining the intensity of the generated GWs. We have simulated decaying primordial acoustic turbulence in three dimensions and make a prediction for the universal shape of the energy spectrum by using its self-similar decay properties and the shape of individual shock waves. The shape for the spectrum is used to determine the time dependence of the fluid kinetic energy and the energy containing length scale at late times. The inertial range power law is found to be close to the classically predicted $k^{-2}$ and approaches it with increasing Reynolds number. The resulting model for the velocity spectrum and its decay in time is combined with the sound shell model assumptions about the correlations of the velocity field to compute the GW power spectrum for flows that decay in less than the Hubble time. The decay is found to bring about a convergence in the spectral amplitude and the peak power law that leads to a power law shallower than the $k^9$ of the stationary case.

gr-qc↗

arXiv2024

A-B transition in superfluid $^3$He and cosmological phase transitions

First order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna (LISA). All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid $^3$He an ideal for test of classical nucleation theory. As Leggett and others have noted the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave (GW) production in the early universe. Here we discuss studies of the AB phase transition dynamics in $^3$He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases.

cond-mat.supr-con↗

arXiv2024

Improved Dirichlet boundary conditions for lattice gauge-fermion theories

Hybrid Monte Carlo (HMC) simulations of lattice gauge theories with fermionic matter rely on the invertibility of the lattice Dirac operator. Near-zero modes of the latter can therefore significantly slow down the update algorithm and cause instabilities. This is in particular a problem when dealing with massless fermions. Homogeneous temporal Dirichlet boundary conditions can be used to remove zero modes from massless lattice Dirac operators, but the standard implementation of these boundary conditions can cause severe finite-volume cutoff effects in regions of parameter space where the physics at the ultraviolet (UV) cutoff scale is dominated by the fermionic instead of the gauge action. In lattice quantum chromodynamics (QCD) this is usually not an issue, as the gauge action dominates the UV physics and the problem does not show up. In studies of beyond standard model (BSM) theories, on the other hand, the finite-volume artifacts can be severe. We have identified the origin of these IR cutoff effects and propose a simple improvement on the homogeneous temporal Dirichlet boundary conditions to prevent them. We demonstrate the benefits of using our improved boundary conditions at the example of SU(2) lattice gauge theory with $N_f=24$ massless Wilson-clover flavors. Due to the large number of fermions in this theory, the boundary-related finite volume artifacts are particularly strong, and the effect from switching from the normal to our improved homogeneous Dirichlet boundary conditions is therefore distinct.

hep-lat↗

arXiv2023

Disentangling the gravity dual of Yang-Mills theory

A construction of a gravity dual to a physical gauge theory requires confronting data. We establish a proof-of-concept for precision holography, i.e., the explicit reconstruction of the dual background metric functions directly from the entanglement entropy (EE) of strip subregions that we extract from pure glue Yang-Mills theory discretized on a lattice. Our main focus is on a three-dimensional Euclidean SU(2) theory in the deconfining phase. Holographic EE suggests, and we find evidence for, that the scaling of the thermal entropy with temperature is to power 7/3 and that it approaches smoothly the critical point, consistent with black hole thermodynamics. In addition, we provide frugal results on the potential between quenched quarks by the computation of the Polyakov loop correlators on the lattice. Holographic arguments pique curiosity in the substratum of Debye screening at strong coupling.

hep-th↗

arXiv2023

Bulk-preventing actions for SU(N) gauge theories

Lattice gauge field theories may suffer from unphysical "bulk" phase transitions at strong lattice gauge coupling. We introduce a one-parameter family of lattice SU(N) gauge actions which, when used in combination with an HMC update algorithm, prevents the appearance of the bulk phase transition. We briefly discuss the (presumed) mechanism behind the prevention of the bulk transition and present test results for different SU(N) gauge groups.

hep-lat↗

arXiv2023

Electroweak Sphaleron in a Magnetic field

Using lattice simulations we calculate the rate of baryon number violating processes, the sphaleron rate, in the Standard Model with an external (hyper)magnetic field for temperatures across the electroweak cross-over, focusing on the broken phase. Additionally, we compute the Higgs expectation value and the pseudocritical temperature. The electroweak cross-over shifts to lower temperatures with increasing external magnetic field, bringing the onset of the suppression of the baryon number violation with it. When the hypermagnetic field reaches the magitude $B_Y \approx 2 T^2$ the cross-over temperature is reduced from $160$ GeV to $145$ GeV. In the broken phase for small magnetic fields the rate behaves quadratically as a function of the magnetic flux. For stronger magnetic fields the rate reaches a linear regime which lasts until the field gets strong enough to restore the electroweak symmetry where the symmetric phase rate is reached.

hep-ph↗

arXiv2022

Holographic spacetime from lattice Yang-Mills theory

Entanglement entropy is a notoriously difficult quantity to compute in strongly interacting gauge theories. Existing lattice replica methods have suffered from a severe signal-to-noise ratio problem, making high-precision studies prohibitively expensive. Our improved lattice method mitigates this situation and allows us to probe holographic predictions for the behavior of entanglement entropies in three- and four-dimensional Yang-Mills theories. We use this data for the numerical reconstruction of holographic bulk metrics.

hep-th↗

arXiv2022

Improved lattice method for determining entanglement measures in SU(N) gauge theories

The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "Rényi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of Rényi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.

hep-lat↗