arXiv subjects

I Jensen

Publications and source records attributed to I Jensen.

5 recordsLinked to original sources

arXiv2017

Polygons pulled from an adsorbing surface

We consider self-avoiding lattice polygons, in the hypercubic lattice, as a model of a ring polymer adsorbed at a surface and either being desorbed by the action of a force, or pushed towards the surface. We show that, when there is no interaction with the surface, then the response of the polygon to the applied force is identical (in the thermodynamic limit) for two ways in which we apply the force. When the polygon is attracted to the surface then, when the dimension is at least 3, we have a complete characterization of the critical force--temperature curve in terms of the behaviour, (a) when there is no force, and, (b) when there is no surface interaction. For the 2-dimensional case we have upper and lower bounds on the free energy. We use both Monte Carlo and exact enumeration and series analysis methods to investigate the form of the phase diagram in two dimensions. We find evidence for the existence of a \emph{mixed phase} where the free energy depends on the strength of the interaction with the adsorbing line and on the applied force.

cond-mat.stat-mech↗

arXiv2014

Analysis of mean cluster size in directed compact percolation near a damp wall

We investigate the behaviour of the mean size of directed compact percolation clusters near a damp wall in the low-density region, where sites in the bulk are wet (occupied) with probability $p$ while sites on the wall are wet with probability $p_w$. Methods used to find the exact solution for the dry case ($p_w=0$) and the wet case ($p_w=1$) turn out to be inadequate for the damp case. Instead we use a series expansion for the $p_w=2p$ case to obtain a second order inhomogeneous differential equation satisfied by the mean size, which exhibits a critical exponent $γ=2$, in common with the wet wall result. For the more general case of $p_w=rp$, with $r$ rational, we use a modular arithmetic method of finding ODEs and obtain a fourth order homogeneous ODE satisfied by the series. The ODE is expressed exactly in terms of $r$. We find that in the damp region $0<r<2$ the critical exponent $γ^{\rm damp}=1$, in common with the dry wall result.

math-ph↗

arXiv1996

Low temperature series expansions for the square lattice Ising model with spin S > 1

We derive low-temperature series (in the variable $u = \exp[-βJ/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We determine the location of the physical critical point and non-physical singularities. The number of non-physical singularities closer to the origin than the physical critical point grows quite rapidly with $S$. The critical exponents at the singularities which are closest to the origin and for which we have reasonably accurate estimates are independent of $S$. Due to the many non-physical singularities, the estimates for the physical critical point and exponents are poor for higher values of $S$, though consistent with universality.

cond-mat↗

arXiv1996

Extrapolation procedure for low-temperature series for the square lattice spin-1 Ising model

The finite-lattice method of series expansions has been combined with a new extrapolation procedure to extend the low-temperature series for the specific heat, spontaneous magnetisation and susceptibility of the spin-1 Ising model on the square lattice. The extended series were derived by directly calculating the series to order 99 (in the variable $u=\exp[-J/k_B T])$ and using the new extrapolation procedure to calculate an additional 13--14 terms.

cond-mat↗

arXiv1996

Directed percolation near a wall

Series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction. The percolation threshold $p_c$ is found to be the same as that for the bulk. However the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by $β_1 = 0.7338 \pm 0.0001$ and $γ_1 = 1.8207 \pm 0.0004$ respectively. On the other hand the exponent $Δ_1=β_1 +γ_1$ characterising the scale of the cluster size distribution is found to be unchanged by the presence of the wall. The parallel connectedness length, which is the scale for the cluster length distribution, has an exponent which we estimate to be $ν_{1\parallel} = 1.7337 \pm 0.0004$ and is also unchanged. The exponent $τ_1$ of the mean cluster length is related to $β_1$ and $ν_{1\parallel}$ by the scaling relation $ν_{1\parallel} = β_1 + τ_1$ and using the above estimates yields $τ_1 = 1$ to within the accuracy of our results. We conjecture that this value of $τ_1$ is exact and further support for the conjecture is provided by the direct series expansion estimate $τ_1= 1.0002 \pm 0.0003$.

cond-mat↗