Related papers: The large $N$ vector model on $S^1\times S^2$

We study the $O(N)$ vector model for scalars with quartic interaction at large $N$ on $S^1\times S^2$ without the singlet constraint. The non-trivial fixed point of the model is described by a thermal mass satisfying the gap equation at…

We have computed through order $\beta^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,\beta)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic…

We propose formulas for the $1/N$ correction to the sphere free energy of theories with 4-fermion interactions, which are conformal for $d>2$. We also propose a formula for the scalar $O(N)$ model. Expanding these formulas in small…

We analyze the real-time dynamics of the large $N$ vector model, focusing on heavy states with energies of the order $N$. In this regime, we demonstrate that interactions become sufficiently strong to produce non-zero condensate of the…

We evaluate the thermal one point function of higher spin currents in the critical model of $U(N)$ complex scalars interacting with a quartic potential and the $U(N)$ Gross-Neveu model of Dirac fermions at large $N$ and strong coupling…

Logarithmic finite-size scaling of the O($n$) universality class at the upper critical dimensionality ($d_c=4$) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems.…

It has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group $O(N)^{q-1}$ agrees with the large $N$ limit of the SYK model. In these notes we investigate aspects of the…

We investigate finite-temperature observables in three-dimensional large $N$ critical vector models taking into account the effects suppressed by $1\over N$. Such subleading contributions are captured by the fluctuations of the…

Using a simple identity between various partial derivatives of the energy of the vector model in 0+0 dimensions, we derive explicit results for the coefficients of the large N expansion of the model. These coefficients are functions in a…

We use the linear $\delta$ expansion, or optimized perturbation theory, to evaluate the effective potential for the two dimensional Gross-Neveu model at finite temperature and density obtaining analytical equations for the critical…

We consider the supersymmetric Wess-Zumino model at large $N$ in $(2+1)$ dimension. We introduce a chemical potential($\mu$) at finite temperature($T$). The non-trivial fixed point of this model is described by a pair of coupled gap…

The classical $n$-vector $\phi^4$ model with $O(n)$ symmetrical Hamiltonian ${\cal H}$ is considered in a $\infty^2\times L$ slab geometry bounded by a pair of parallel free surface planes at separation $L$. The temperature-dependent…

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (also known as the O(N) symmetric Heisenberg classical spin model or the as the lattice O(N) nonlinear sigma model) on the…

We propose a numerical method to estimate one-point functions and the free-energy density of conformal field theories at finite temperature by solving the Kubo-Martin-Schwinger condition for the two-point functions of identical scalars. We…

We revisit the relation between the spherical model of Berlin-Kac and the spin $O(N)$ model in the limit $N \to \infty$, and explain how they are connected via the discrete Gaussian free field (GFF). Using probabilistic limit theorems and…

We calculate the anomalous dimensions of higher spin singlet currents in the critical $O(N)$ vector model at order $1/N^2$. The results are shown to be in agreement with the four-loop perturbative computation in $\phi^4$ theory in…

For the classical N-vector model, with arbitrary N, we have computed through order \beta^{17} the high temperature expansions of the second field derivative of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body centered…

We study the thermal partition function of level $k$ U(N) Chern-Simons theories on $S^2$ interacting with matter in the fundamental representation. We work in the 't Hooft limit, $N,k\to\infty$, with $\lambda = N/k$ and $\frac{T^2…

The large-$N$ nonlinear $O(N)$, $CP^{N-1}$ $\sigma$ models are studied on $R^2 \times S^1$. The $N$-components scalar fields of the models are supposed to acquire a phase $e^{i2\pi\delta}$ $(0\leq \delta <1)$, along the circulation of the…

We discuss two types of quantum mechanical models that couple large numbers of Majorana fermions and have orthogonal symmetry groups. In models of vector type, only one of the symmetry groups has a large rank. The large $N$ limit is taken…