Generic power laws in higher-dimensional lattice models with multidirectional hopping
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| Format: | Preprint |
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2025
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| _version_ | 1866917038110277632 |
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| author | Hazra, Animesh Chakraborty, Tanmoy Mukherjee, Anirban Pradhan, Punyabrata |
| author_facet | Hazra, Animesh Chakraborty, Tanmoy Mukherjee, Anirban Pradhan, Punyabrata |
| contents | We show that, on a $d-$dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with {\it multidirectional} hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter values $-$ even {\it far} from phase transition point, if any. The key idea for generating the algebraic decay is the notion of {\it multidirectional} hopping, which means that several chunks of masses, or several particles, can hop out simultaneously from a lattice site in multiple directions, consequently breaking detailed balance. Notably, the systems we consider are described by a continuous-time Markov process, are diffusive, {\it lattice-rotation symmetric}, spatially homogeneous and thus have {\it no} net mass current. Using hydrodynamic and exact microscopic theory, we show that, for spatial dimensions $d > 1$, the steady-state static density-density and ``activity''-density correlation functions in the thermodynamic limit typically decay as $\sim 1/r^{(d+2)}$ at large distance $r=|{\bf r}|$; the strength of the power law is exactly calculated for several models and expressed in terms of the density-dependent bulk-diffusion coefficient and Onsager matrix (or, mobility tensor). In particular, our theory explains why center-of-mass-conserving dynamics, used to model novel disordered {\it hyperuniform} state of matter, result in generic long-ranged correlations. However, in a restricted parameter regime, the correlations can also be short ranged and are characterized through the Onsager matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic power laws in higher-dimensional lattice models with multidirectional hopping Hazra, Animesh Chakraborty, Tanmoy Mukherjee, Anirban Pradhan, Punyabrata Statistical Mechanics We show that, on a $d-$dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with {\it multidirectional} hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter values $-$ even {\it far} from phase transition point, if any. The key idea for generating the algebraic decay is the notion of {\it multidirectional} hopping, which means that several chunks of masses, or several particles, can hop out simultaneously from a lattice site in multiple directions, consequently breaking detailed balance. Notably, the systems we consider are described by a continuous-time Markov process, are diffusive, {\it lattice-rotation symmetric}, spatially homogeneous and thus have {\it no} net mass current. Using hydrodynamic and exact microscopic theory, we show that, for spatial dimensions $d > 1$, the steady-state static density-density and ``activity''-density correlation functions in the thermodynamic limit typically decay as $\sim 1/r^{(d+2)}$ at large distance $r=|{\bf r}|$; the strength of the power law is exactly calculated for several models and expressed in terms of the density-dependent bulk-diffusion coefficient and Onsager matrix (or, mobility tensor). In particular, our theory explains why center-of-mass-conserving dynamics, used to model novel disordered {\it hyperuniform} state of matter, result in generic long-ranged correlations. However, in a restricted parameter regime, the correlations can also be short ranged and are characterized through the Onsager matrix. |
| title | Generic power laws in higher-dimensional lattice models with multidirectional hopping |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2503.18365 |