Complex Materials Theory Group

Welcome to the Torquato Group!

Professor Salvatore Torquato

Professor of Chemistry

Email Prof. Torquato : Curriculum Vitae : Wikipedia Page : More information

Pictured are (left) a quantum spin liquid (QSL) phase and (right) its structure factor (proportional to the scattering intensity in the scattering experiments). Chen et al. unveiled a hidden structural property of classical and quantum spin liquids known as hyperuniformity (i.e., infinite-wavelength density fluctuations are anomalously suppressed in these systems), and discovered new metrics that can distinguish a quantum spin liquid phase from other proximate quantum phases. Their findings may help identify potential QSL candidates, and represent the first example of the emergence of disordered hyperuniformity in strongly correlated, long-range entangled quantum systems. Click here to read the full paper. Click here to read a popular account of the work. Click here to watch a recently-given introductory lecture on the concept of hyperuniformity.

Our research group is based at Princeton University in the Department of Chemistry and Princeton Materials Institute. We also have affiliations with three other departments/programs: Physics, Applied and Computational Mathematics, and Mechanical & Aerospace Engineering. Professor Torquato has been a Faculty Fellow in the Princeton Center for Theoretical Science

Research work in the group is centered in statistical mechanics and soft condensed matter theory. Current topics of interest include unusual low-temperature states of matter, packing problems, structure and bulk properties of colloids, liquids, glasses, quasicrystals and crystals, hyperuniformity, novel photonic materials, discrete geometry, self-assembly theory, disordered heterogeneous materials, optimization in materials science, cancer modeling, and biophysics. For more information, please see our News page.

PCTS workshop - December 9-11, 2026 - Jadwin Hall 407, Princeton University, Princeton, NJ
We recently computed effective transport and mechanical properties of model two-phase heterogeneous materials with varying degrees of disorder.
Schematic illstrating how electric waves propagate through a 2D stealthy hyperuniform two-phase dielectric medium within a perfect transparency interval.
We used novel statistical analyses to study many-body correlations in various phases of water for a range of temperatures across length scales.
We developed metrics for quantifying degrees of phase-mixing and separation across length and time scales in heterogeneous materials and scalar fields.
We developed an improved methodology to generate disordered stealthy hyperuniform point patterns of unprecendented size and accuracy.
New numerical simulations suggest that ideal maximally random jammed packings of hard spheres for spatial dimensions 3 and higher become more hyperuniform as the dimension increases.
Novel numerical methods reveal equilibrium states (right) corresponding to hyperuniform nonequilibrium pair statistics (left).
Extensive numerical simulations suggest that the photonic band gaps for special disordered "highly stealthy hyperuniform" dielectric networks persist in the thermodynamic limit.
"Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales" is Published in Physical Review X. See the Publications page to read this paper, or click the image for links to several popular accounts of this article.
A recording of Professor Torquato's seminar on hyperuniformity given at the Institute for Advanced Study on February 25th 2022.
Simulated steady state flow through a Gaussian random field microstructure.
Three different "classes" of degenerate Debye random media.
A maximally random jammed (MRJ) sphere packing and its associated Voronoi cells.
Metastable and glassy water phase diagram in the temperature-pressure plane.
Photonic networks: (a) the crystal diamond network and (b) the disordered nearly hyperuniform network model.
Schematic showing how the critical pore size of a dispersion of hard disks can be determined from the corresponding Voronoi diagram.
Schematic showing the preparation of a jammed packing of curved triangles via the stochastic adaptive shrinking cell algorithm, as well as the associated spectral density of the packing.
For any nonzero temperature, Henderson's theorem is not practically applicable if very similar pair correlation functions correspond to distinctly different pair potentials.