#paperOfTheDay : "From nondegenerate conducting polymers to dense matter in the massive Gross-Neveu model" from 2005.
I shared a few papers about the Gross-Neveu model before: It is a renormalizable #quantumFieldTheory in 1+1 dimensions consisting of fermions with a 4-fermion-interaction vertex (which would not be renormalizable in 4 dimension). It is asymptotically free at high energies, and has a discrete chiral symmetry psi -> gamma_5 psi (where psi is the fermion field) when it is massless. However, under certain conditions a mass is dynamically generated, which leads to a quite interesting phase diagram: There is a massive and a massless phase, and also an intermediate non-homogeneous "crystal" phase.
This all is about the GN model as a relativistic field theory. However, the same (i.e. mathematically equivalent) model arises in condensed matter #physics as an effective model for the behaviour of e.g. polymers. A simple example are polymers consisting of long chains of carbon with alternating single and double bonds, C-C=C-C=... (with appropriate hydrogen atoms attached). The discrete chiral symmetry corresponds to flipping the location of the bonds, which might or might not yield an equivalent molecule (which, in field theory language, means that the mass is intact or broken). The present paper re-derives the ground state of the massive GN model from this polymer perspective, by solving the corresponding Schrödinger equations and finding the minimal energy solution. The results are fully compatible with field theory. As the authors put it, they foster the relation between "Phys Rev D" (fields) and "Phys Rev B" (condensed matter) communities. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.72.105008

Monday's #paperOfTheDay is "Renormalization Group flows between Gaussian Fixed Points" from 2022. This preprint concerns scalar #quantumFieldTheory with different choices of the propagator. Conventionally, one has (in a massless theory) a propagator of the form 1/p^2, corresponding to a kinetic term of second derivatives. However, there could be (i.e. it is generated by quantum fluctuations) also 2-point interactions proportional to more derivatives, in particular a fourth derivative. This raises the question whether one can equivalently use that term as the propagator, i.e. assign the value 1/p^4 to edges in #FeynmanIntegral s, and use the other term as an interaction vertex. In principle that works, but it leads to a number of technical issues such as having states with negative norm (ghosts).
The present preprint takes a different perspective: At low energies (consider e.g. plane waves with long wavelength), a fourth derivative will be numerically small, while it dominates at high energy. One can therefore view the transition from one choice of propagator to the other as a #renormalization group flow that starts in the UV with a fourth derivative, and arrives at a second derivative in the IR. An analogous argument has long been known for a mass term (i.e. 2-point term with zero derivatives): In the UV, the kinetic term p^2 determines the behaviour of the field (e.g. UV convergence of Feynman integrals), whereas at low energy, every propagator is essentially constant 1/m^2. Notice that all these transitions are taken at fixed spacetime dimension, whereas #tropicalFieldTheory is an analogous limit to zero derivatives in zero dimensions, which gives a different result.
https://arxiv.org/abs/2207.10596v1

The #paperOfTheDay is "Exponents for the excluded volume problem as derived by the Wilson Method" from 1972. This one-page letter makes one elementary, but far-reaching observation: The O(N)-invariant scalar #quantumFieldTheory , which had a few months before been treated by Wilson in terms of dimensional regularization, has a special interpretation when N=0. Namely, one assigns to every #FeynmanGraph a "symmetry factor", which is a polynomial in N. The coefficient of N^k in this polynomial counts how many ways there are to decompose the 4-valent vertices of the graph such that one obtains exactly k cycles. If one sets N=0, all that remains is the constant term: It counts the ways of decomposing the graph without forming any cycle.
One is interested in the statistical behaviour of non-crossing paths on a lattice, called a self-excluding walk. This can be studied with the methods of statistical #physics . One introduces a Boltzmann-type weight exp(-n*p), where p is a parameter (analogous to the inverse temperature or the Planck constant), and n is the length of a self-excluding walk. Let N_n be the number of different such walks (for a fixed size of the lattice, or counted relative to the lattice size), then the sum of N_n*exp(-n*p) is analogous to a partition function, or path integral. Hence, it can be analyzed perturbatively with Feynman integrals, namely those mentioned above of the O(N) theory at N=0. This way, one obtains, for example, the critical exponents.
https://www.sciencedirect.com/science/article/pii/0375960172901491

Application is open for #Integrability , Dualities and Deformations 2026, this year in Wrocław, Poland. Topics are at the intersection of #mathematics and #physics , ranging from #quantumFieldTheory to #Hopf algebras. The deadline for contributed abstracts and early registration is 1 May.
https://indico.global/event/16474/

In July, there is the YETI 2026 #summerSchool for PhD students from the UK, to foster collaboration between theory and experiments in collider and particle #physics phenomenology and #quantumFieldTheory . It takes place in #Durham UK, meals and accommodation are provided free of charge.
https://conference.ippp.dur.ac.uk/event/1551/

#PaperOfTheDay is "Full phase diagram of the massive Gross-Neveu model" from 2006.
The Gross-Neveu model is a #quantumFieldTheory of fermions in two spacetime dimensions. In the absence of a bare mass term, it has a discrete chiral symmetry (a few days ago I shared a paper where that symmetry is promoted to a continuous symmetry by adding a second interaction term). The present paper, conversely, is about the case where the mass is non-zero. Then, chiral symmetry is broken.
They consider the theory from a #thermodynamics perspective, where the variables are temperature (i.e. the Planck constant in quantum field language), chemical potential (i.e. a constant offset to energy), and the mass of the particle. Using a clever ansatz, they are able to compute the full phase diagram of the Gross-Neveu field as function of the three variables. As had long been known, if the bare mass vanishes, then the model generates a dynamic mass for the fermion at low enough temperature and chemical potential. It had previously been believed that at non-vanishing bare mass, there would be a discontinuous change in the effective mass from large to small as the temperature is increased. The central result of the present paper is that this is false: Instead, in the boundary region, there is another phase where the field is spacially non-homogeneous, it forms a periodic crystal. Below, one has a heavy fermion, above the fermion is light, and the new phase is something different altogether.
https://www.sciencedirect.com/science/article/abs/pii/S0003491605002915

As is well known, the Einstein-Hilbert action of general #relativity, i.e. Einstein #Gravity, can not be "simply" turned into a #quantumFieldTheory in the usual perturbative way. Over the decades, this has given rise to dozens of proposed solutions, either by modifying the Einstein-Hilbert action (e.g. introducing a fourth derivative term), or by modifying quantum field theory (e.g. replace it by #stringTheory ), or by examining the possibility for fully non-perturbative quantum field theory (e.g. #asymptoticSafety studies via functional renormalization).
One of the approaches that somehow combines the first and second viewpoint is #causalSetTheory . There, one assumes that spacetime is fundamentally discrete, not like a lattice, but more like a random #graph and the edges in this graph represent causal relations (i.e. being in the future or past light cone). Viewed from afar, this might look like a 4-dimensional spacetime, but looked closely, there is only discrete structure. The edges (causal connections) do not only join nearest neighbours, but can reach far along the lightcone, this gives rise to non-trivial effects, and it makes it surprisingly hard to simulate such a causal set (I've tried that once, but without much success).
The causal sets community has produced a 1 hour video to explain these concepts to a general audience interested in #physics
https://www.youtube.com/watch?v=5EoZE1rOHAo

The #paperOfTheDay for Monday was "Unitarity, stability, and loops of unstable ghosts" from 2019.
In #quantumFieldTheory , (bosonic) particles have a propagator of the form i/(p^2-m^2), where p is the momentum and m the mass. This propagator decays quadratically as p becomes large, and when m=0, it reflects a force that decays like 1/r^2 in 4-dimensional #physics spacetime (e.g. electromagnetic forces). Classically, it corresponds to Lagrangian equations of motion which are second-order in time derivatives.
Having fourth time derivatives in a Lagrangian, conversely, classically leads to the Ostrogradsky problems I mentioned a few weeks ago. In a quantum theory, it gives a propagator like i/(p^4). The present paper studies the special case of propagators i/(p^2 -p^4/m^2), where m is some reference mass. A central point is that this can on the one hand be interpreted as a propagator with exotic momentum dependence, but equivalently also as a sum of propagators of two distinct particles, i/p^2 - i/(p^2-m^2). The second of these has a negative sign, it is a "ghost" particle. Nonetheless, many computations work as usual and give sensible results. In particular, if the theory contains interactions, the ghost is not a stable physicle state, but unstable, and therefore it does not appear in unitarity relations or asymptotic scattering states. The conclusion is that such a theory makes perfect sense if done correctly, with one exception: It violates microcausality (on short scales related to the lifetime of the ghost). If that is allowed in nature is ultimately a question to be answered by experiments.
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.100.105006

#paperOfTheDay "Large N solution of generalized Gross-Neveu model with two coupling constants" from 2009.
The Gross-Neveu model is a #quantumFieldTheory of fermionic fields with a 4-fermion interaction vertex. Such theory would be non-renormalizable in 4-dimensional nature, but the Gross-Neveu model is usually considered in 2 dimensions. Its interaction term is of the form (psibar*psi)^2, where psibar is the Hermitian conjugate spinor to psi (i.e. this interaction vertex has 2 incoming and 2 outgoing fermions). The theory has a global discrete symmetry psi -> gamma_5*psi, which effectively exchanges psi and psibar (gamma_5 is the 5th Dirac matrix).
On the other hand, one can augment this model with a second interaction term of the form (psibar*i*gamma_5*psi)^2. If both terms appear with the same coupling constant, the full model (assuming that there is no mass term for the fermion) has a continuous symmetry psi -> exp(i*alpha*gamma_5)psi. This is called "chiral symmetry", and the continuous parameter alpha gives rise to a massless Goldstone boson. The so-defined model is called Nambu-Jona-Lasinio model.
The present paper investigates the transition between GN and NJL model, that is, starting from only the Gross-Neveu interaction term, and gradually adding the other term until both of them are equally strong and the NJL model is recovered. Indeed, this results in a continuous interpolation between the two models. One can also view this as a version of chiral symmetry breaking "through interaction", which is different from the more familiar version of chiral symmetry breaking where the fermions simply get a non-zero mass term.
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.80.125038