ICTS:30039

Phase transitions in a system of long hard rods on a lattice

APA

(2024). Phase transitions in a system of long hard rods on a lattice. SciVideos. https://youtube.com/live/eogiSl68gvs

MLA

Phase transitions in a system of long hard rods on a lattice. SciVideos, Oct. 28, 2024, https://youtube.com/live/eogiSl68gvs

BibTex

          @misc{ scivideos_ICTS:30039,
            doi = {},
            url = {https://youtube.com/live/eogiSl68gvs},
            author = {},
            keywords = {},
            language = {en},
            title = {Phase transitions in a system of long hard rods on a lattice},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30039 see, \url{https://scivideos.org/icts-tifr/30039}}
          }
          
Deepak Dhar
Talk numberICTS:30039

Abstract

A system of hard rigid rods of length $k \gg1$ on hypercubic lattices in dimensions $d \geq2$, is known to undergo two phase transitions when chemical potential is increased: from a low-density phase to an intermediate density nematic phase, and on further increase to a high-density phase with no nematic order. I will present non-rigorous arguments to support the conjecture that for large $k$, the second phase transition is a first-order transition with a discontinuity in density in all dimensions greater than $1$. The chemical potential at the transition is $\approx A k \ln k$ for large $k$, and that the density of uncovered sites drops from a value $\approx B (\ln k)/ k^2$ , to a value of order $\exp(−ck)$, where $c$ is some constant, across the transition. We conjecture that these results are asymptotically exact, and $A = B= 1$, in all dimensions $d ≥ 2$.