Zero-temperature limits of the local and global thermodynamic quantities in the nine-membered antiferromagnetic s = 3/2 spin ring are investigated by means of numerical exact diagonalization.An anisotropic Heisenberg model with tunable bond defect reecting continuously varying topology (from closed to open ring) is exploited.The frustrated and non-frustrated phases are identied in the ground-state phase diagram determined by a bond-defect strength and magnetic eld.Near the phase boundaries signicance of the thermal uctuations aecting the estimates of the local magnetic quantities found earlier at T = 1 K is revealed.For the global quantities the eects of thermal uctuations are found much weaker.A sequence of the local magnetic moments is analysed and their experimental verication at the edges of the non-frustrated and within the entire frustrated phase is suggested at suciently low temperature.Zero-temperature limits of the local and global thermodynamic quantities in the nine-membered antiferromagnetic s = 3/2 spin ring are investigated by means of numerical exact diagonalization.An anisotropic Heisenberg model with tunable bond defect reecting continuously varying topology (from closed to open ring) is exploited.The frustrated and non-frustrated phases are identied in the ground-state phase diagram determined by a bond-defect strength and magnetic eld.Near the phase boundaries signicance of the thermal uctuations aecting the estimates of the local magnetic quantities found earlier at T = 1 K is revealed.For the global quantities the eects of thermal uctuations are found much weaker.A sequence of the local magnetic moments is analysed and their experimental verication at the edges of the non-frustrated and within the entire frustrated phase is suggested at suciently low temperature.

Acta Physica Polonica AMay 1, 20122 citations

Bulk and surface phase transitions in the three-dimensional O(4) spin model

Youjin Deng

We investigate the $O(4)$ spin model on the simple-cubic lattice by means of the Wolff cluster algorithm. Using the toroidal boundary condition, we locate the bulk critical point at coupling ${K}_{c}=0.935\phantom{\rule{0.2em}{0ex}}856(2)$ , and determine the bulk thermal magnetic renormalization exponents as ${y}_{t}=1.337\phantom{\rule{0.2em}{0ex}}5(15)$ and ${y}_{h}=2.482\phantom{\rule{0.2em}{0ex}}0(2)$ , respectively. The universal ratio $Q={⟨{m}^{2}⟩}^{2}∕⟨{m}^{4}⟩$ is also determined as 0.9142(1). The precision of these estimates significantly improves over that of the existing results. Then, we simulate the critical $O(4)$ model with two open surfaces on which the coupling strength ${K}_{1}$ can be varied. At the ordinary transitions, the surface magnetic exponent is determined as ${y}_{h1}^{(\mathrm{o})}=1.020\phantom{\rule{0.2em}{0ex}}2(12)$ . Further, we find a so-called special surface transition at $\ensuremath{\kappa}={K}_{1}∕K\ensuremath{-}1=1.258(20)$. At this point, the surface thermal exponent ${y}_{t1}^{(\mathrm{s})}$ is rather close to zero, and we cannot exclude that the corresponding surface transition is Kosterlitz-Thouless-like. The surface magnetic exponent is ${y}_{h1}^{(\mathrm{s})}=1.816(2)$ .We investigate the $O(4)$ spin model on the simple-cubic lattice by means of the Wolff cluster algorithm. Using the toroidal boundary condition, we locate the bulk critical point at coupling ${K}_{c}=0.935\phantom{\rule{0.2em}{0ex}}856(2)$, and determine the bulk thermal magnetic renormalization exponents as ${y}_{t}=1.337\phantom{\rule{0.2em}{0ex}}5(15)$ and ${y}_{h}=2.482\phantom{\rule{0.2em}{0ex}}0(2)$, respectively. The universal ratio $Q={⟨{m}^{2}⟩}^{2}∕⟨{m}^{4}⟩$ is also determined as 0.9142(1). The precision of these estimates significantly improves over that of the existing results. Then, we simulate the critical $O(4)$ model with two open surfaces on which the coupling strength ${K}_{1}$ can be varied. At the ordinary transitions, the surface magnetic exponent is determined as ${y}_{h1}^{(\mathrm{o})}=1.020\phantom{\rule{0.2em}{0ex}}2(12)$. Further, we find a so-called special surface transition at $\ensuremath{\kappa}={K}_{1}∕K\ensuremath{-}1=1.258(20)$. At this point, the surface thermal exponent ${y}_{t1}^{(\mathrm{s})}$ is rather close to zero, and we cannot exclude that the corresponding surface transition is Kosterlitz-Thouless-like. The surface magnetic exponent is ${y}_{h1}^{(\mathrm{s})}=1.816(2)$.

Physical Review EMay 19, 200638 citations

Ground and thermal state properties of model spin systems

Amit Kumar Pal

Jan 1, 20130 citations

Critical behaviour of spin models : A transfer-matrix approach

Yolanda M. M. Knops

Oct 27, 19940 citations

The spin model. III. Analysis of high temperature series expansions of some thermodynamic quantities in two dimensions

Jos Rogiers, Ernst W. Grundke, Donald D. Betts

In this paper we report analyses of high temperature series expansions for the spin [Formula: see text] XY model on the triangular and square lattices. Quantities for which series are analyzed include the fluctuation in the transverse magnetization, fourth order fluctuations in the same quantity, second and fourth moments of the transverse spin–spin correlations, specific heat, and entropy. The evidence favours a phase transition at a finite temperature with conventional power law critical singularities. Scaling seems to hold but hyperscaling seems to be violated. Estimates for critical exponents include γ = 2.50 ± 0.3. Δ = 2.38 ± 0.2, and ν = 143 ± 0.10. The specific heat exhibits no singular behaviour at Tc.In this paper we report analyses of high temperature series expansions for the spin [Formula: see text] XY model on the triangular and square lattices. Quantities for which series are analyzed include the fluctuation in the transverse magnetization, fourth order fluctuations in the same quantity, second and fourth moments of the transverse spin–spin correlations, specific heat, and entropy. The evidence favours a phase transition at a finite temperature with conventional power law critical singularities. Scaling seems to hold but hyperscaling seems to be violated. Estimates for critical exponents include γ = 2.50 ± 0.3. Δ = 2.38 ± 0.2, and ν = 143 ± 0.10. The specific heat exhibits no singular behaviour at Tc.

Canadian Journal of PhysicsOct 1, 197956 citations

We investigate the

O(4)

spin model on the simple-cubic lattice by means of the Wolff cluster algorithm. Using the toroidal boundary condition, we locate the bulk critical point at coupling

{K}_{c}=0.935\phantom{\rule{0.2em}{0ex}}856(2)

, and determine the bulk thermal magnetic renormalization exponents as

{y}_{t}=1.337\phantom{\rule{0.2em}{0ex}}5(15)

and

{y}_{h}=2.482\phantom{\rule{0.2em}{0ex}}0(2)

, respectively. The universal ratio

Q={⟨{m}^{2}⟩}^{2}∕⟨{m}^{4}⟩

is also determined as 0.9142(1). The precision of these estimates significantly improves over that of the existing results. Then, we simulate the critical

O(4)

model with two open surfaces on which the coupling strength

{K}_{1}

can be varied. At the ordinary transitions, the surface magnetic exponent is determined as

{y}_{h1}^{(\mathrm{o})}=1.020\phantom{\rule{0.2em}{0ex}}2(12)

. Further, we find a so-called special surface transition at $\ensuremath{\kappa}={K}_{1}∕K\ensuremath{-}1=1.258(20)$. At this point, the surface thermal exponent

{y}_{t1}^{(\mathrm{s})}

is rather close to zero, and we cannot exclude that the corresponding surface transition is Kosterlitz-Thouless-like. The surface magnetic exponent is

{y}_{h1}^{(\mathrm{s})}=1.816(2)