CakePHP - virtual tree

Page.php

<?php
class Page extends AppModel{
  public $useTable = 'objects';

	public $actsAs = array(
		'Tree' => array( 'recursive' => 0 )
    );

public $virtualFields	= array(
		'lft' => 'Tree.lft',
		'rght' => 'Tree.rght',
		'parent_id' => 'Tree.parent_id',
	)

  public $hasOne = array(
		'Tree' => array(
			'className' 	=> 'Tree',
			'foreignKey'	=> 'object_id',
			'dependent'    => true
		),
	);

}

schema

CREATE TABLE `objects` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `site_id` int(11) DEFAULT NULL,
  `type` varchar(255) COLLATE utf8_persian_ci NOT NULL,
  `model` varchar(255) COLLATE utf8_persian_ci NOT NULL,
  `lang` varchar(5) COLLATE utf8_persian_ci NOT NULL,
  `name` varchar(255) COLLATE utf8_persian_ci NOT NULL,
  `alias` varchar(255) COLLATE utf8_persian_ci NOT NULL,
  `home` tinyint(1) NOT NULL DEFAULT '0',
  `status` tinyint(1) NOT NULL DEFAULT '1',
  `content_count` int(11) DEFAULT '0',
  `service_count` int(11) DEFAULT '0',
  `created` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,
  `modifed` timestamp NOT NULL DEFAULT '0000-00-00 00:00:00',
  PRIMARY KEY (`id`),
  KEY `fk_objects_sites_1` (`site_id`)
) ENGINE=InnoDB AUTO_INCREMENT=14 DEFAULT CHARSET=utf8 COLLATE=utf8_persian_ci;

CREATE TABLE `objects_tree` (
  `object_id` int(11) NOT NULL,
  `parent_id` int(11) DEFAULT NULL,
  `lft` int(11) NOT NULL,
  `rght` int(11) DEFAULT NULL,
  PRIMARY KEY (`object_id`),
  KEY `fk_objects_sites_1` (`object_id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 COLLATE=utf8_persian_ci;

Tree.php

<?php
class Tree extends AppModel{
  
	public $useTable = 'objects_tree';



	public $belongsTo = array(
		'belongsTo' => array(
			'className' 	=> 'Page',
			'foreignKey'	=> 'object_id',
		
		),
	);
    
}