Phase coexistence and spatial correlations in reconstituting<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-mer models

Chatterjee, Amit Kumar; Daga, Bijoy; Mohanty, P. K.

doi:10.1103/physreve.94.012121

Cited by 4 publications

(4 citation statements)

References 62 publications

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“…In fact, if all three auxiliaries were same i.e. A(n) = A(n) = Ā(n), then (34) reduces to the familiar cancellation scheme studied here in (5) with R l = R r = 1 and correspondingly one obtains a matrix product steady state for totally asymmetric hoping model with hop rate u R = u(n i−1 , n i , n i+1 ) and u L = 0, a model which we have already discussed in the previous section.…”

Section: Examplementioning

confidence: 99%

“…Soon after being introduced in context of TASEP [20], MPA has found enormous applications in different branches of physics. MPA [33] has been very helpful in calculating spatial correlation functions for exclusion processes with point objects [8] as well as for extended objects [34] in one dimension. Study of relations between algebraic Bethe ansatz [35] and matrix product states for stochastic Markovian models in 1D [36] and the same for spin- 1 2 Heisenberg chains [37] brought calculational convenience and also gave good physical insight to the problems.…”

Section: Introductionmentioning

confidence: 99%

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Matrix product states for interacting particles without hardcore constraints

Chatterjee¹,

Mohanty²

2017

J. Phys. A: Math. Theor.

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Abstract. We construct matrix product steady state for a class of interacting particle systems where particles do not obey hardcore exclusion, meaning each site can occupy any number of particles subjected to the global conservation of total number of particles in the system. To represent the arbitrary occupancy of the sites, the matrix product ansatz here requires an infinite set of matrices which in turn leads to an algebra involving infinite number of matrix equations. We show that these matrix equations, in fact, can be reduced to a single functional relation when the matrices are parametric functions of the representative occupation number. We demonstrate this matrix formulation in a class of stochastic particle hopping processes on a one dimensional periodic lattice where hop rates depend on the occupation numbers of the departure site and its neighbors within a finite range; this includes some well known stochastic processes like, totally asymmetric zero range process, misanthrope process, finite range process and partially asymmetric versions of the same processes but with different rate functions depending on the direction of motion.

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Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Matrix product states for interacting particles without hardcore constraints

Chatterjee¹,

Mohanty²

2017

J. Phys. A: Math. Theor.

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“…These models are rather simple having trivial integer exponents. Some variations of CLG models also show continuously varying critical exponents or multi-critical behaviour [27,28]. Non-DP behaviour in these models can not be blamed to presence of the conserved density because the same dynamics on a ladder geometry lead to an absorbing transition belonging to DP class [21].…”

Section: Introductionmentioning

confidence: 99%

“…APT in presence of a conserved field [23,24] has been a subject of interest in recent years. The conserved lattice gas (CLG) model [25,26] and some of its extensions [27,28] are exactly solvable in one dimension * arijit.chatterjee@saha.ac.in † pk.mohanty@saha.ac.in and they provide clear examples of non-DP behaviour. These models are rather simple having trivial integer exponents.…”

Section: Introductionmentioning

confidence: 99%

Multichain models of conserved lattice gas

Chatterjee

Mohanty

2017

Phys. Rev. E

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Conserved lattice gas (CLG) models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents β = 1 = ν = η whereas the same on a ladder belong to directed percolation (DP)universality. We conjecture that additional stochasticity in particle transfer is a relevant perturbation and its presence on a ladder force the APT to be in DP class. To substantiate this we introduce a class of restricted conserved lattice gas models on a multi-chain system (M × L square lattice with periodic boundary condition in both directions), where particles which have exactly one vacant neighbor are active and they move deterministically to the neighboring vacant site. We show that for odd number of chains , in the thermodynamic limit L → ∞, these models exhibit APT at ρc = with β = 1, 2 for M = 2, 4 respectively, and β = 3 for M ≥ 6. We illustrate this unusual critical behaviour analytically using a transfer matrix method.

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Zero range and finite range processes with asymmetric rate functions

Chatterjee

Mohanty

2017

J. Stat. Mech.

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Abstract. We introduce and solve exactly a class of interacting particle systems in one dimension where particles hop asymmetrically. In its simplest form, namely asymmetric zero range process (AZRP), particles hop on a one dimensional periodic lattice with asymmetric hop rates; the rates for both right and left moves depend only on the occupation at the departure site but their functional forms are different. We show that AZRP leads to a factorized steady state (FSS) when its rate-functions satisfy certain constraints. We demonstrate with explicit examples that AZRP exhibits certain interesting features which were not possible in usual zero range process. Firstly, it can undergo a condensation transition depending on how often a particle makes a right move compared to a left one and secondly, the particle current in AZRP can reverse its direction as density is changed. We show that these features are common in other asymmetric models which have FSS, like the asymmetric misanthrope process where rate functions for right and left hops are different, and depend on occupation of both the departure and the arrival site. We also derive sufficient conditions for having cluster-factorized steady states for finite range process with such asymmetric rate functions and discuss possibility of condensation there.Keywords: Zero-range processes, Non-equilibrium processes, Exact results Zero range and finite range processes with asymmetric rate functions 2

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Phase coexistence and spatial correlations in reconstitutingk-mer models

Cited by 4 publications

References 62 publications

Matrix product states for interacting particles without hardcore constraints

Matrix product states for interacting particles without hardcore constraints

Multichain models of conserved lattice gas

Zero range and finite range processes with asymmetric rate functions

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