arXiv subjects

Christoph P. Hofmann

Publications and source records attributed to Christoph P. Hofmann.

At least 19 recordsLinked to original sources

arXiv2021

Emergence of Spin Order in Two-Dimensional Quantum Heisenberg Antiferromagnets

Counterintuitive order-disorder phenomena emerging in antiferromagnetically coupled spin systems have been reported in various studies. Here we perform a systematic effective field theory analysis of two-dimensional bipartite quantum Heisenberg antiferromagnets subjected to either mutually aligned -- or mutually orthogonal -- magnetic and staggered fields. Remarkably, in the aligned configuration, the finite-temperature uniform magnetization $M_T$ grows as temperature rises. Even more intriguing, in the orthogonal configuration, $M_T$ first drops, goes through a minimum, and then increases as temperature rises. Unmasking the effect of the magnetic field, we furthermore demonstrate that the finite-temperature staggered magnetization $M^H_s$ and entropy density -- both exhibiting non-monotonic temperature dependence -- are correlated. Interestingly, in the orthogonal case, $M^H_s$ presents a maximum, whereas in mutually aligned magnetic and staggered fields, $M^H_s$ goes through a minimum. The different behavior can be traced back to the existence of an "easy XY-plane" that is induced by the magnetic field in the orthogonal configuration.

cond-mat.str-el↗

arXiv2021

Diamagnetic and Paramagnetic Phases in Low-Energy Quantum Chromodynamics

While it is known that the QCD vacuum in a magnetic background exhibits both diamagnetic and paramagnetic characteristics in the low-energy domain, a systematic investigation of the corresponding phases emerging in the pion-dominated regime is still lacking. Here, within two-flavor chiral perturbation theory, taking into account the pion-pion interaction, we analyze the subtle interplay between zero- and finite-temperature portions in the magnetization and magnetic susceptibility. The dependence of the magnetic susceptibility on temperature and magnetic field strength in the paramagnetic and diamagnetic phase is non-monotonic. Our low-energy analysis complements lattice QCD that is currently operating at higher temperatures and stronger magnetic fields.

hep-ph↗

arXiv2020

Thermomagnetic Properties of QCD

We explore the low-energy regime of quantum chromodynamics subjected to an external magnetic field by deriving the two-loop representations for the entropy density and the magnetization within chiral perturbation theory (CHPT). At fixed temperature, the entropy density drops when the magnetic field becomes stronger. The magnetization induced at finite temperature is negative in the entire parameter region accessible by CHPT. We also point out that the enhancement of the finite-temperature part in the quark condensate is correlated with the decrease of the entropy density.

hep-ph↗

arXiv2020

Antiferromagnetic Dispersion Relations and Nature of Magnon Pressure

We derive higher-order corrections in the magnon dispersion relations for two- and three-dimensional antiferromagnets exposed to magnetic and staggered fields that are mutually aligned. "Dressing" the magnons is the prerequisite to separate the low-temperature representation of the pressure into a piece due to noninteracting magnons and a piece that corresponds to the magnon-magnon interaction. Both in two and three spatial dimensions, the interaction in the pressure turns out to be attractive. While concrete figures refer to the spin-$\frac{1}{2}$ square-lattice and the spin-$\frac{1}{2}$ simple cubic lattice antiferromagnet, our results are valid for arbitrary bipartite geometry.

cond-mat.str-el↗

arXiv2020

Spin Order and Entropy in Antiferromagnetic Films Subjected to Magnetic Fields

Using systematic effective field theory, we explore the properties of antiferromagnetic films subjected to magnetic and staggered fields that are either mutually aligned or mutually orthogonal. We provide low-temperature series for the entropy density in either case up to two-loop order. Invoking staggered, uniform and sublattice magnetizations of the bipartite antiferromagnet, we investigate the subtle order-disorder phenomena in the spin arrangement, induced by temperature, magnetic and staggered fields -- some of which are quite counterintuitive. In the figures we focus on the spin-$\frac{1}{2}$ square-lattice antiferromagnet, but our results are valid for any other bipartite two-dimensional lattice.

cond-mat.str-el↗

arXiv2020

Chiral Perturbation Theory Analysis of the Quark Condensate in a Magnetic Field

We present two-loop results for the quark condensate in an external magnetic field within chiral perturbation theory using coordinate space techniques. At finite temperature, we explore the impact of the magnetic field on the pion-pion interaction in the quark condensate for arbitrary pion masses and derive the correct weak magnetic field expansion in the chiral limit. At zero temperature, we provide the complete two-loop representation for the vacuum energy density and the quark condensate.

hep-ph↗

arXiv2020

Pion Pressure in a Magnetic Field

While the partition function for QCD in a magnetic field $H$ has been calculated before within chiral perturbation theory up to two-loop order, our investigation relies on an alternative representation for the Bose functions which allows for a clear-cut expansion of thermodynamic quantities in the chiral limit. We first focus on the pion-pion interaction in the pressure and show that -- depending on magnetic field strength, temperature and pion mass -- it may be attractive or repulsive. We then analyze the thermodynamic properties in the chiral limit and provide explicit two-loop representations for the pressure in the weak magnetic field limit $|qH| \ll T^2$.

hep-ph↗

arXiv2020

Order Parameter and Magnetization of Antiferromagnets in Mutually Parallel Staggered and Magnetic Fields

We explore the behavior of the order parameter and the magnetization of antiferromagnetic solids subjected to mutually parallel staggered and magnetic fields. The effective field theory analysis of the partition function is taken up to the two-loop level, where the magnon-magnon interaction comes into play. These interaction effects, however, are small. A phenomenon that comes rather unexpectedly is that the finite-temperature magnetization increases with temperature when the strengths of the staggered and magnetic field are held constant.

cond-mat.str-el↗

arXiv2019

Thermodynamics of Antiferromagnetic Solids in Magnetic Fields

We analyze the thermodynamic properties of antiferromagnetic solids subjected to a combination of mutually orthogonal uniform magnetic and staggered fields. Low-temperature series for the pressure, order parameter and magnetization up to two-loop order in the effective expansion are established. We evaluate the self-energy and the dispersion relation of the dressed magnons in order to discuss the impact of spin-wave interactions on thermodynamic observables.

cond-mat.str-el↗

arXiv2019

Square-Lattice Antiferromagnet Subjected to a Magnetic Field Aligned with the Order Parameter

The thermal properties of antiferromagnetic films -- in particular, the square-lattice antiferromagnet -- subjected to an external magnetic field pointing into the direction of the staggered magnetization are explored. The effective field theory analysis of the free energy density is carried out to two-loop order. While the emphasis is on finite temperature, we also discuss the behavior of the magnetization and staggered magnetization at zero temperature. Our results imply that the staggered magnetization increases in presence of the magnetic field -- reminiscent of magnetic catalysis. Most remarkably, if staggered and magnetic field strength are kept fixed, the magnetization initially grows when temperature increases.

cond-mat.str-el↗

arXiv2017

Mermin-Wagner at the Crossover Temperature

Mermin-Wagner excludes spontaneous (staggered) magnetization in isotropic ferromagnetic (antiferromagnetic) Heisenberg models at finite temperature in spatial dimensions $d \le 2$. While the proof relies on the Bogoliubov inequality, here we illuminate the theorem from an effective field theory point of view. We estimate the crossover temperature $T_c$ and show that, in weak external fields $H$, it tends to zero: $T_c \propto \sqrt{H}$ ($d=1$) and $T_c \propto 1/|\ln H|$ ($d=2$). Including the case $d$=3, we derive upper bounds for the (staggered) magnetization by combining microscopic and effective perspectives -- unfortunately, these bounds are not restrictive.

cond-mat.str-el↗

arXiv2017

Quark Condensate in a Weak Magnetic Field

The low-temperature representation for the quark condensate in a weak magnetic field $H$ is known up to two-loop order. Remarkably, at one-loop order, the published series for the quark condensate in the chiral limit and $H \ll T^2$ are inconsistent. Using an alternative representation for the kinematical Bose functions, we derive the series to arbitrary order in $H/T^2$, and also determine which of the published results is correct.

hep-ph↗

arXiv2017

Two-loop free energy of three-dimensional antiferromagnets in external magnetic and staggered fields

Using a model-independent low-energy effective field theory, we calculate the free energy of three-dimensional antiferromagnets in a combination of mutually perpendicular external magnetic and staggered fields at the next-to-next-to-leading, two-loop order. Renormalization is carried out analytically, and the renormalization group invariance of the result is checked explicitly. The free energy is thus expressed solely in terms of temperature, the external fields, and a set of low-energy coupling constants, to be determined by experiment or by matching to the microscopic model of a given concrete material.

cond-mat.str-el↗

arXiv2017

Magnetic Catalysis in Antiferromagnetic Films

We study the low-temperature behavior of antiferromagnets in two spatial dimensions that are subjected to a magnetic field oriented perpendicular to the staggered magnetization order parameter. The evaluation of the partition function is carried to two-loop order within the systematic effective Lagrangian technique. Low-temperature series that are valid in weak magnetic and staggered fields are derived for the pressure, staggered magnetization, and magnetization. Remarkably, at $T$=0, the staggered magnetization is enhanced by the magnetic field, implying that the phenomenon of magnetic catalysis also emerges in antiferromagnetic films.

cond-mat.str-el↗

arXiv2016

Quantum Chromodynamics, Antiferromagnets and XY Models from a Unified Point of View

Antiferromagnets and quantum XY magnets in three space dimensions are described by an effective Lagrangian that exhibits the same structure as the effective Lagrangian of quantum chromodynamics with two light flavors. These systems all share a spontaneously broken internal symmetry O($N$) $\to$ O($N$-1). Although the respective scales differ by many orders of magnitude, the general structure of the low-temperature expansion of the partition function is the same. In the nonabelian case, logarithmic terms of the form $T^8 \ln T$ emerge at three-loop order, while for $N$=2 the series only involves powers of $T^2$. The manifestation of the Goldstone boson interaction in the pressure, order parameter, and susceptibility is explored in presence of an external field.

hep-ph↗

arXiv2016

Interpreting Numerical Measurements in Fixed Topological Sectors

For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are feasible only within individual sectors. The challenge is to assemble such restricted measurements in a way that leads to a substantiated approximation to the fully fledged result, which would correspond to the correct sampling over the entire set of configurations. We test an approach for such a topological summation, which was suggested by Brower, Chandrasekharan, Negele and Wiese. Under suitable conditions, energy levels and susceptibilities can be obtained to a good accuracy, as we demonstrate for O(N) models, SU(2) Yang-Mills theory, and for the Schwinger model.

hep-lat↗

arXiv2016

Thermodynamics of the $d$=3+1 Quantum XY Model

Within effective field theory we explore the properties of the $d$=3+1 quantum XY model at low temperatures and in weak magnetic or staggered fields. For this parameter regime only few results appear to be known, and furthermore are restricted to one-loop order. In the present study we systematically analyze the thermodynamics of the $d$=3+1 quantum XY model up to three-loop order. In the low-temperature expansion of the free energy density, the free Bose gas term of order $T^4$ receives corrections of order $T^6$ and $T^8$. The discussion also includes the pressure, (staggered) magnetization and susceptibility. In particular, we show how these quantities are influenced by the spin-wave interaction. We then compare our findings with those for the quantum XY model in $d$=2+1.

cond-mat.str-el↗

arXiv2015

Measuring the Topological Susceptibility in a Fixed Sector

For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( < Q^2 > - < Q >^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of chi_t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear sigma-models and in 2d Abelian gauge theory yield accurate results for chi_t, which confirm that the method is applicable. We also obtain promising results in 4d SU(2) Yang-Mills theory, which suggest the applicability of this method in QCD.

hep-lat↗