Publications Davidson Noby Joseph

2026

Phys. Rev. E
Exact critical-temperature bounds for two-dimensional Ising models

Davidson Noby Joseph, and Igor Boettcher

Phys. Rev. E, – Published May 2026

Abstract arXiv DOI bib

We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a universal number that is solely determined by the largest coordination number on the lattice. Crucially, these bounds are tight in some cases such as the Honeycomb, Square, and Triangular lattices. We prove the bounds using the Feynman-Kac-Ward formalism, confirm their validity for a selection of over two hundred lattices, and construct a two-dimensional lattice with 24-coordinated sites and record high critical temperature.
@article{svhn-yfv1, title = {Exact critical-temperature bounds for two-dimensional Ising models}, author = {Joseph, Davidson Noby and Boettcher, Igor}, journal = {Phys. Rev. E}, pages = {}, year = {2026}, month = may, publisher = {American Physical Society}, doi = {10.1103/svhn-yfv1}, url = {https://link.aps.org/doi/10.1103/svhn-yfv1}, }
Under Review
Families of planar lattices with arbitrarily high $T_{\rm c}$ for the ferromagnetic Ising model

Davidson Noby Joseph, Connor M. Walsh, and Igor Boettcher

May 2026

Abstract arXiv bib

We construct families of periodic tessellations of the plane with arbitrarily high critical temperature, $T_{\rm c}$, for the classical ferromagnetic Ising model. Our approach is motivated by recently found exact bounds, which imply that large values of $T_{\rm c}$ require large values of the maximal coordination number of the lattice, $q_{\rm max}$. We create such lattices through iterative triangulation and derive explicit expressions for their $T_{\rm c}$. Furthermore, we show that $T_{\rm c}$ for these families scales asymptotically as $T_{\rm c}/J \sim A \ln q_{\rm max}$ with a universal prefactor $A=2/\ln 2$. We introduce a function $T_{\rm c}^*(q_{\rm max})$ that we conjecture to be an upper bound on the critical temperature of any periodic tessellation of the plane. We show that the family of so-called Apollonian lattices, which are derived from the Triangular lattice through iterative triangulation, saturates this bound. The lattices discussed in this work are relevant for theoretical questions of optimality in network systems and may be realized experimentally in Coherent Ising Machines or topoelectric circuits in the future.
@misc{joseph2026familiesplanarlatticesarbitrarily, title = {Families of planar lattices with arbitrarily high $T_{\rm c}$ for the ferromagnetic Ising model}, author = {Joseph, Davidson Noby and Walsh, Connor M. and Boettcher, Igor}, year = {2026}, eprint = {2605.10017}, archiveprefix = {arXiv}, primaryclass = {cond-mat.stat-mech}, url = {https://arxiv.org/abs/2605.10017}, }
Am J. Phys

A simple quantum dot: Numerical and variational solutions

Connor M. Walsh, Ian MacPherson, Davidson Noby Joseph, and 4 more authors

Am. J. Phys 94, 465-475 – Published Jun 2026

Abstract arXiv DOI

We describe a simple quantum dot that consists of two crossed two-dimensional troughs. As such there is no potential well; nonetheless, this geometry gives rise to a bound state, centered on the point at which these troughs cross one another. This problem is interesting both because the existence of a bound state may surprise students and because it can be solved using a variety of computational techniques, including matrix mechanics, finite differences, and mode matching. We present these methods and show how the mode-matching method in this case provides the most accurate solution to the problem. Additionally, the mode-matching method can be used to generate a simple wave function that yields the lowest energy known to date to arise out of an analytical variational solution for this problem.

2025

Phys. Rev. E
Walking on Archimedean lattices: Insights from Bloch band theory

Davidson Noby Joseph, and Igor Boettcher

Phys. Rev. E 112, 044118 – Published Oct 2025

Abstract arXiv DOI bib

Returning walks on a lattice are sequences of moves that start at a given lattice site and return to the same site after $n$ steps. Determining the total number of returning walks of a given length $n$ is a typical graph-theoretical problem with connections to lattice models in statistical and condensed matter physics. We derive analytical expressions for the returning walk numbers on the eleven two-dimensional Archimedean lattices by developing a connection to the theory of Bloch energy bands. We benchmark our results through an alternative method that relies on computing the moments of adjacency matrices of large graphs, whose construction we explain explicitly. As condensed matter physics applications, we use our formulas to compute the density of states of tight-binding models on the Archimedean lattices and analytically determine the asymptotics of the return probability. While the Archimedean lattices provide a sufficiently rich structure and are chosen here for concreteness, our techniques can be generalized straightforwardly to other two- or higher-dimensional Euclidean lattices.
@article{1fvj-91v6, title = {Walking on Archimedean lattices: Insights from Bloch band theory}, author = {Joseph, Davidson Noby and Boettcher, Igor}, journal = {Phys. Rev. E}, volume = {112}, issue = {4}, pages = {044118}, numpages = {29}, year = {2025}, month = oct, publisher = {American Physical Society}, doi = {10.1103/1fvj-91v6}, url = {https://link.aps.org/doi/10.1103/1fvj-91v6}, }