Moire systems offer an exciting playground to study many-body effects of strongly correlated electrons in regimes that are not easily accessible conventional material settings. Motivated by a recent experiment on $\text{WSe}_2/\text{WS}_2$ moire bilayers [Y. Tang et al., Nature 579, 353-358 (2020)], which realizes triangular superlattice with small hopping (of approximately 10 Kelvin), tunable ...

We study the frustration properties of Ising model on a decorated triangular lattice with an arbitrary number decorating spins all bonds in framework exact analytical approach based Kramers–Wannier transfer matrix method. Expressions for entropy, heat capacity, and spontaneous magnetization are obtained, including residual (zero-temperature) entropy system. The existence magnetic frustrations s...

We study complex-temperature singularities of the Ising model on the triangular and honeycomb lattices. We first discuss the complex-T phases and their boundaries. From exact results, we determine the complex-T singularities in the specific heat and magnetization. For the triangular lattice we discuss the implications of the divergence of the magnetization at the point u = − 3 (where u = z2 = e...

A point set X in the Euclidean plane is called a k-distance set if there are exactly k different distances between distinct points in X. Let g(k) denote the maximum number of points in a k-distance set. For example, it is well known that g(1) = 3, realized by the three vertices of an equilateral triangle. Erdős and Fishburn [2] introduce the problem of determining g(k). To date only six values ...

Connection between discrete and continuum models of polymerized (tethered) surfaces has been investigated by applying a transfer matrix method to a discrete rigid-bond triangular lattice, which is allowed to fold on itself along its bonds in a two-dimensional embedding space. As its continuum counterpart, the model has an extensive entropy and the mean squared distance between two sites of a fo...

We study percolation and the random cluster model on the triangular lattice with 3-body interactions. Starting with percolation, we generalize the star–triangle transformation: We introduce a new parameter (the 3-body term) and identify configurations on the triangles solely by their connectivity. In this new setup, necessary and sufficient conditions are found for positive correlations and thi...

We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behavior of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail (ISAT) model on that lattice, the...

We show that the motion of a single hole in the infinite-U Hubbard model with frustrated hopping leads to weak metallic antiferromagnetism of kinetic origin. An intimate relationship is demonstrated between the simplest versions of this problem in one and two dimensions, and two of the most subtle many body problems, namely, the Heisenberg Bethe ring in one dimension and the two-dimensional tri...

We analyze the partition function of the dimer model on an M×N triangular lattice wrapped on a torus obtained by Fendley, Moessner, and Sondhi [Phys. Rev. B 66, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by a conformal field theory having a central charge c=-2. The shift exponent for the specific heat is found to depend on t...